Free Printable Exponent Rules/Logarithms/Interest Formulas Review

1.

$5^3\cdot5^4$

a)

$5^2$

b)

$5^7$

c)

$5^6$

d)

$5^{10}$

2.

$\frac{5^3}{5^2}$

a)

$5$

b)

$5^5$

c)

$5^2$

d)

$5^8$

3.

$\left(7^3\right)^4$

a)

$7^{12}$

b)

$7^7$

c)

$7^1$

4.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

5.

a)

w^-3

b)

w³

c)

w²

d)

w^-13

6.

$\frac{9x^2}{3x^{ }}=$

a)

$3x^2$

b)

$3x$

c)

$9x$

d)

$6x$

7.

$\left(ab^2\right)^8$ =

a)

$ab^{16}$

b)

$a^8b^{16}$

c)

$a^9b^{10}$

d)

$ab^{10}$

8.

Evaluate using the quotient rule:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

9.

-3xy³ . (4xy)²

a)

-12x³y⁵

b)

-48x²y⁴

c)

-48x³y⁵

d)

-12x²y⁶

10.

a)

A

b)

B

c)

C

d)

D

11.

Simplify the expression. $-\frac{y^{-4}z^2\cdot y^0z^2}{\left(2z^{-4}\right)^3}$

a)

$-\frac{z^{16}}{8y^4}$

b)

$-y^{24}x^{18}$

c)

$\frac{y^3}{x}$

d)

$\frac{x^4z^6}{4y^7}$

12.

Select the exponent that makes the equation true.

a)

1

b)

2

c)

3

d)

6

e)

24

13.

$\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)$

a)

$4$

b)

$-5$

c)

$-3$

d)

$-1$

14.

$\left(\sqrt{13}+2\sqrt{5}\right)^2$

a)

$31+4\sqrt{65}$

b)

$37+\sqrt{65}$

c)

$2\sqrt{65}+33$

d)

$33+4\sqrt{65}$

15.

$\ Simplify:\ \ \ 6\sqrt{2}\cdot5\sqrt{14}$

a)

$32\sqrt{7}$

b)

$60\sqrt{7}$

c)

$2\sqrt{7}$

d)

$30\sqrt{7}$

16.

$\sqrt{96ab^4}$

a)

$16\sqrt{6ab}$

b)

$2a\sqrt{6ab^2}$

c)

$4b^2\sqrt{6a}$

d)

$4b^4\sqrt{6a}$

17.

Simplify

a)

$3x^2y^2z\sqrt[3]{3yz}$

b)

$3xyz\sqrt[3]{xy^2}$

c)

$3xyz$

d)

Can not simplify further

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

A

b)

B

c)

C

d)

D

20.

Simplify:
(4√5)(7√7)

a)

28√35

b)

4√35

c)

140√7

d)

Cannot be multiplied.

21.

Convert 10^(x+5)=100 to logarithmic form.

a)

log₁₀₀=x+5

b)

log(x+5)=100

c)

log(100)=x+5

d)

log_(x+5)(100)=10

22.

Write in exponential form:
log ₃ 6561 = 8

a)

3⁸ = 6561

b)

8³ = 6561

c)

3⁶⁵⁶¹= 8

d)

8⁶⁵⁶¹ = 3

23.

Write the following equation in exponential form:
log₂⅛ = -3

a)

2^⅛ = -3

b)

(⅛)^-3 = 2

c)

2^-3 = ⅛

d)

(-3)^⅛= 2

24.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

25.

If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.

a)

1.25mg

b)

1.25g

c)

10g

d)

10mg

26.

Rachel invested $2,700 in a savings account earning 7% simple interest. If she invests for 2 years, how much money will she have in total?

a)

$3,078

b)

$378

c)

$40,500

d)

$4536

27.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

28.

Damara invests $3500 at 2% compounded continuously for 5 years. How much will she have in her account after 5 years?

a)

$3868.10

b)

$3886.10

c)

$3688.10

d)

$3286.10

29.

Convert to logarithmic form: $3^7=y$

a)

$\log_3y=7$

b)

$\log_73=y$

c)

$\log_y3=7$

d)

$\log_37=y$

30.

Write 10⁴= 10000 in logarithmic form.

a)

log₁₀ 4 = 10000

b)

log₁₀₀₀₀ 4 = 10

c)

log₁₀ 10000 = 4

d)

log₄ 10000 = 10

31.

Convert 2^x+6=10 to logarithmic form

a)

log₄(x)=2

b)

log₂(4)=x

c)

log₂(10)=6

d)

log₂(x)=4

32.

Rewrite in exponential form. $\log_{6\ }t=m$

a)

$m^t=6$

b)

$t^m=6$

c)

$6^t=m$

d)

$6^m=t$

33.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

34.

a)

A

b)

B

c)

C

d)

D

35.

The coyote population in western North Carolina is increasing at a rate of 3.5% per year. In 2020, there were 700 coyotes in western North Carolina. How many coyotes are there projected to be in 2025 using the current rate of growth?

a)

776 coyotes

b)

784 coyotes

c)

831 coyotes

d)

812coyotes

36.

The half-life of Iridium-182 is 15 minutes. How much of a 240 milligram sample of Iridium-182 is remaining after an hour?

a)

30 milligrams

b)

60 milligrams

c)

7.5 milligrams

d)

15 milligrams

37.

When Loofa was born, her parents put $8,000 into a college fund account that earned 9% simple interest. What will her account total after 18 years?

a)

$720

b)

$20,960

c)

$1,080

d)

$12,960

38.

Emilio borrows $1200 from a bank with 8% simple interest per year. How much will he have to pay back total in 2 years?

a)

$150

b)

$192

c)

$1350

d)

$1392

39.

Your 3 year investment of $20,000 received 5.2% interest compounded annually. What is your total return?

a)

$23,285.05

b)

$3,285.05

c)

$2,385

d)

$32,285

40.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

41.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

42.

Ashleigh put some money into an account paying 4.5% compounded continuously for 10 years. She now has $3567.91 in the account. How much money did she start the account with?

a)

$2275

b)

$2725

c)

$2572

d)

$3275

43.

Abhasra invests $8,911 in a retirement account with a fixed annual interest rate of 7.71% compounded continuously. What will the account balance be after 20 years?

a)

$41,649.38

b)

$51,649.38

c)

$61,649.38

d)

$71,649.38

Exponent Rules/Logarithms/Interest Formulas Review

Total questions: 43

Worksheet time: 1hrs 3mins

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