Go through the Math in Focus Grade 8 Workbook Answer Key Chapter 1 Lesson 1.1 Exponential Notation to finish your assignments.

## Math in Focus Grade 7 Course 3 A Chapter 1 Lesson 1.1 Answer Key Exponential Notation

### Math in Focus Grade 8 Chapter 1 Lesson 1.1 Guided Practice Answer Key

**Identify the base and exponent in each expression.**

Question 1.

2^{3}

Answer:

Base is 2 and exponent is 3,

Explanation:

2^{3} = 2 • 2 • 2,

Here base is 2 and exponent is 3.

Question 2.

(-5)^{4}

Answer:

Base is -5 and exponent is 4.

Explanation:

(-5)^{4} = -5 • -5 • -5 • -5,

Here base is -5 and exponent is 4.

**Tell whether each statement is correct. If it is incorrect, state the reason.**

Question 3.

6^{3} = 6 • 6 • 6

Answer:

Statement 6^{3} = 6 • 6 • 6 is correct,

Explanation:

Given 6^{3} = 6 • 6 • 6 is correct statement .

Question 4.

5 • 5 = 2^{5}

Answer:

Statement 5 • 5 =2^{5 }is incorrect,

Explanation:

Given Statement 5 • 5 =2^{5 }is incorrect reason is

5 • 5 is 5^{2 }not 2^{5}.

**Write in exponential notation.**

Question 5.

Answer:

Explanation:

Given 2 • 2 • 2 • 2 • 2 • 2 so exponential notation is

2 times 6 equals to 2^{6 } the base is 2 and the exponent is 6.

Question 6.

Answer:

Explanation:

Given (-4) • (-4) • (-4) so exponential notation is

(-4) times 3 equals to (-4)^{3 } the base is (-4) and the exponent is 3.

Question 7.

Answer:

Explanation:

Given (2/3)y • (2/3)y • (2/3)y • (2/3)y so exponential notation is

(2/3)y times 4 equals to ((2/3)y)^{4 } the base is (2/3)y and the exponent is 4.

**Expand and evaluate each expression.**

Question 8.

Answer:

Explanation:

Given 3^{4} evaluating as 3 • 3 • 3 • 3, therefore the base 3 is used as a factor of four times

and evaluated as 81.

Question 9.

Answer:

Explanation:

Given (-5)^{3} evaluating as -5 • -5 • -5, therefore the base -5 is used as a factor of three times

and evaluated as -125.

Question 10.

Answer:

Explanation:

Given (3/4)^{3} evaluating as (3/4) • (3/4) • (3/4),

therefore the base (3/4) is used as a factor of three times

and evaluated as (27/64).

**Write the prime factorization of each number in exponential notation.**

Question 11.

625

Answer:

Explanation:

Given to find the prime factorization of 625 in exponential notation,

So 625 has last digit 5 and 5 itself is prime 5 has factors 1 and 5 only,

When divided 625 with 5 we get remainder 125,

In 125 the last digit is 5 again the factors of 5 are 1,5,

Now dividing 125 with 5 we get remainder 25 and also

25 has last digit 5 factors of 25 are 1,5 leaving remainder of 5,

5 itself is prime so the last digit is 5,

So 625 = 5 • 125,

= 5 • 5 • 25,

= 5 • 5 • 5 • 5

= (5)^{4}

Solving 625 using prime factorization method we got

the exponential notation as (5)^{4}.

Question 12.

Answer:

Explanation:

Given to find the prime factorization of 630 in exponential notation,

So 630 has last digit as 0 as 0 is not prime and next

numbers are 21 when divided by 3 we get remainder 70,

Now 70 is divisible by 7 we will get remainder 10,

10 is not a prime number,

so 630 = 3 • 210,

630 = 3 • 3 • 70,

630 = 3 • 3 • 7 • 10,

630 = (3)^{2 }• 7 • 10,

Solving 625 using prime factorization method we got the

exponential notation as (3)^{2 }• 7 • 10.

**Solve. Show your work.**

Question 13.

Karen ate at a restaurant. One day later, Karen told three friends about the restaurant.

The day after that, each of the friends Karen had told about the restaurant told

three more friends about the restaurant.

If this pattern continued, how many friends were told about

the restaurant five days after Karen ate there?

Answer:

81 friends were told about

the restaurant five days after Karen ate there,

Explanation:

Karen ate at a restaurant, One day later Karen told three friends about the restaurant.

The day after that each of the friends Karen had told about

the restaurant told three more friends about the restaurant.

If this pattern continued friends that were told about

the restaurant five days after Karen ate there at a restaurant

Explanation:

Number of friends who were told about the restaurant five days after

Karen ate there = Initial number of people who knew about the restaurant •

Rate of word-of-mouth referrals over 5 days

people were told about the restaurant 5 days after Karen ate there.

Question 14.

Dewin, at age 25, invests $2,000 in his retirement account.

It will earn 6% interest, compounded yearly.

How much will be in his account when he retires at age 65?

Answer:

A = $21,914.91

A = P + I where

P (principal) = $2,000.00

I (Interest) = $19,914.91

Explanation:

### Math in Focus Course 3A Practice 1.1 Answer Key

**Identify the base and exponent in each expression.**

Question 1.

10^{5}

Answer:

Base is 10 and exponent is 5,

Explanation:

(10)^{5} = 10 • 10 • 10 • 10 • 10,

Here base is 10 and exponent is 5.

Question 2.

(-7)^{5}

Answer:

Base is -7 and exponent is 5.

Explanation:

-7 • -7 • -7 • -7 • -7,

Here base is -7 and exponent is 5.

Question 3.

(0.2)^{4}

Answer:

Base is 0.2 and exponent is 4.

Explanation:

0.2 • 0.2 • 0.2 • 0.2,

Here base is 0.2 and exponent is 4.

**Tell whether each statement is correct. If it is incorrect, state the reason.**

Question 4.

24^{3} = 2 • 4 • 4 • 4

Answer:

Statement is incorrect,

Explanation:

Statement 24^{3} is incorrect,

As base is 24 and exponent is 3

24^{3} = 24 • 24 • 24 not 24^{3} ≠ 2 • 4 • 4 • 4.

Question 5.

(-2)^{4} = -2 • -2 • -2 • -2

Answer:

Statement is correct,

Explanation:

Given (-2)^{4} here base is -2 and exponent is 4,

so (-2)^{4} = -2 • -2 • -2 • -2.

Question 6.

\(\left(\frac{4}{5}\right)^{5}\) = \(\frac{4}{5}\) • \(\frac{4}{5}\)

• \(\frac{4}{5}\) • \(\frac{4}{5}\) • \(\frac{4}{5}\)

Answer:

Statement is correct,

Explanation:

Given \(\left(\frac{4}{5}\right)^{5}\) here base is

\(\left(\frac{4}{5}\right)^{5}\) and exponent is 5.

**Write in exponential notation.**

Question 7.

24^{3} = 2 • 4 • 4 • 4

Answer:

Statement is incorrect,

Explanation:

Statement 24^{3} is incorrect,

As base is 24 and exponent is 3

24^{3} = 24 • 24 • 24 not 24^{3} ≠ 2 • 4 • 4 • 4.

Question 8.

(-2)^{4} = -2 • -2 • -2 • -2

Answer:

Statement is correct,

Explanation:

Given (-2)^{4} here base is -2 and exponent is 4,

so (-2)^{4} = -2 • -2 • -2 • -2.

**Write in exponential notation.**

Question 9.

\(\frac{1}{3}\) • \(\frac{1}{3}\)

Answer:

\(\left(\frac{1}{3}\right)^{2}\),

Explanation:

Given \(\frac{1}{3}\) • \(\frac{1}{3}\) exponential

notation is equal to \(\left(\frac{1}{3}\right)^{2}\).

Question 10.

5 • 5 • 5 • 5

Answer:

5 • 5 • 5 • 5 = 5^{4},

Explanation:

Given 5 • 5 • 5 • 5 exponential notation is equal to 5^{4},

base is 5 and exponent is 4.

Question 11.

(-2) • (-2) • (-2)

Answer:

(-2) • (-2) • (-2) = (-2)^{3},

Explanation:

Given (-2) • (-2) • (-2) exponential notation is equal to (-2)^{3}

base is (-2) and exponent is 3.

Question 12.

0.12 • 0.12 • 0.12 • 0.12 • 0.12

Answer:

0.12 • 0.12 • 0.12 • 0.12 • 0.12 = (0.12)^{5},

Explanation:

Given 0.12 • 0.12 • 0.12 • 0.12 • 0.12 exponential notation is equal to (0.12)^{5}

base is 0.12 and exponent is 5.

Question 13.

a • a • a

Answer:

a • a • a = (a)^{3},

Explanation:

Given a • a • a exponential notation is equal to (a)^{3}

base is a and exponent is 3.

Question 14.

mn • mn • mn • mn • mn

Answer:

mn • mn • mn • mn • mn = (mn)^{5},

Explanation:

Given mn • mn • mn • mn • mn exponential notation is equal to (mn)^{5}

base is mn and exponent is 5.

**Expand and evaluate each expression.**

Question 15.

2^{3}

Answer:

2^{3} = 2 • 2 • 2,

Explanation:

Given expression 2^{3} upon evaluating we get 2 • 2 • 2.

Question 16.

\(\left(\frac{3}{8}\right)^{4}\)

Answer:

Given expression \(\left(\frac{3}{8}\right)^{4}\) upon evaluting

we get \(\frac{3}{8}\) • \(\frac{3}{8}\)

• \(\frac{3}{8}\) • \(\frac{3}{8}\).

Question 17.

10^{4}

Answer:

10^{4} = 10 • 10 • 10 • 10,

Explanation:

Given expression 10^{4} upon evaluating we get 10 • 10 • 10 • 10.

Question 18.

-3.4^{4}

Answer:

-3.4^{4} = -3.4 • -3.4 • -3.4 • -3.4,

Explanation:

Given expression -3.4^{4} upon evaluating we get -3.4 • -3.4 • -3.4 • -3.4.

**Write the prime factorization of each number ¡n exponential notation.**

Question 19.

125

Answer:

Explanation:

Given to find the prime factorization of 125 in exponential notation,

So 125 has last digit 5 and 5 itself is prime 5 has factors 1 and 5 only,

When divided 125 with 5 we get remainder 125,

In 125 the last digit is 5 again the factors of 5 are 1,5,

Now dividing 125 with 5 we get remainder 25 and also

25 has last digit 5 factors of 25 are 1,5 leaving remainder of 5,

5 itself is prime so the last digit is 5,

So 125 = 5 • 25,

= 5 • 5 • 5,

= 5 • 5 • 5

= (5)^{3}

Solving 125 using prime factorization method we got

the exponential notation as (5)^{3}.

Question 20.

4,802

Answer:

4802 We are given the number:

4802 = 2 ∙ 2401 The last digit is 2, therefore the number is divisible by 2:

= 2 ∙ 7 ∙ 343 The last digit doubled 2, subtracted from 240 leads to 238, which is divisible by 7.

Therefore 2401 is divisible by 7:

= 2 ∙ 7 ∙ 7 ∙ 49

The last digit doubled 6, subtracted from 34 leads to 28, which is divisible by 7.

Therefore 343 is divisible by 7:

= 2 • 7 • 7 • 7 • 7 49 is divisible by 7:

4802 = 2 • 7^{4} we simplify

4802 = 2 • 7^{4}

Question 21.

91,125

Answer:

**Order the following expressions from least to greatest.**

Question 22.

-5^{2}, (-5)^{2}, and -2^{5}

Answer:

Least to greatest -2^{5}, (-5)^{2}, and -5^{2},

Explanation:

According to the order (Brackets, Order, Division, Multiplication,

Addition, Subtraction) the following given expressions from

least to greatest -2^{5}, (-5)^{2}, and -5^{2}.

Question 23.

-4^{3}, -3^{4}, and (-3)^{4}

Answer:

Least to greatest -3^{4}, (-3)^{4}, and -4^{3},

Explanation:

According to the order (Brackets, Order, Division, Multiplication,

Addition, Subtraction) the following given expressions from

least to greatest -4^{3}, (-3)^{4}, and -3^{4}**.**

**Solve. Show your work.**

Question 24.

Barnard’s Star is approximately 10,000,000,000,000,000 meters from the Sun.

Epsilon Eridani is at a distance of about 100,000,000,000,000,000 meters from the Sun.

Write each distance as 10 raised to a power.

Answer:

Barnard’s Star is approximately 10^{16 }meters from the Sun.

Epsilon Eridani is at a distance of about 10^{17 }meters from the Sun,

Explanation:

Given Barnard’s Star ¡s approximately 10,000,000,000,000,000 meters from the Sun.

Epsilon Eridani is at a distance of about 100,000,000,000,000,000 meters from the Sun.

Each distance as 10 raised to power is Barnard’s Star ¡s approximately 10^{16 }meters from the Sun.

Epsilon Eridani is at a distance of about 10^{17 }meters from the Sun.

Question 25.

Use the formula A = P(1 + r)^{n} to find out how much $500 would be worth in

20 years if it increases by 8% each year.

Answer:

The amount increases in 20 years is $2,463.40,

Explanation:

Question 26.

Jen cut a piece of paper in half and threw away one half.

She cut the remaining paper in half and threw away one half.

She continued doing this until she had a piece of paper whose area was \(\frac{1}{32}\) as

great as the area of the original piece of paper. How many cuts did she make?

Answer:

Jen made 5 cuts of the original piece of paper,

Explanation:

Given Jen cut a piece of paper in half and threw away one half.

She cut the remaining paper in half and threw away one half.

She continued doing this until she had a piece of paper whose area was

\(\frac{1}{32}\) as great as the area of the original piece of paper.

Number of cuts and many cuts she made are

Since Jen cut a piece of paper in half and threw away one half it becomes

\(\frac{1}{2}\) and \(\frac{1}{2}\) then

She cut the remaining paper in half and threw away one half so

again \(\frac{1}{2}\) and \(\frac{1}{2}\) and so on

till she got \(\frac{1}{32}\) as denominator is 32

So \(\left(\frac{1}{2}\right)^{5}\),

therefore, Jen made 5 cuts of the original piece of paper.