Free Printable Unit 6 Review: Exponents

1.

Simplify

\left(5x^2y\right)\left(2x^3y^5\right)

a)

$10x^5y^6$

b)

$7x^5y^6$

c)

$10x^5y^5$

d)

$10x^6y^5$

2.

Simplify

\frac{15x^6y^3}{5x^3y^7}

a)

$10x^3y^4$

b)

$\frac{5x^3}{y^4}$

c)

$\frac{x^9}{5y^4}$

d)

$\frac{1}{5x^3y^4}$

3.

Which expression is not equivalent to

3^{-2}

?

a)

$\frac{1}{3^2}$

b)

$\frac{1}{9}$

c)

$-6$

d)

$0.\overline{11}$

4.

If

f\left(x\right)=3\left(2\right)^x

, then what is

f\left(0\right)

?

a)

0

b)

2

c)

3

d)

5

5.

Simplify $\left(2x^{-2}y^7\right)^2$

a)

$4y^9$

b)

$\frac{1}{4x^4y^9}$

c)

$4x^4y^{14}$

d)

$\frac{4y^{14}}{x^4}$

6.

You uploaded a video to TikTok and all of sudden it starts going viral. On the day you first posted it, 20 people saw it. Every day after that the number of views tripled. Which function represents the total number of views after n number of days?

a)

$f\left(x\right)=20\left(3\right)^x$

b)

$f\left(x\right)=3\left(20\right)^x$

c)

$f\left(x\right)=20+3x$

d)

$f\left(x\right)=20\left(3x\right)$

7.

The population in a small town is represented by the formula $f\left(n\right)=6000\left(2.5\right)^x$ . According to the model, check all that are true.

a)

The population is increasing

b)

The initial population is 6000

c)

The population is growing at 2.5%

d)

The population of the small town after 5 years will be 75,000.

8.

What is 25% of 75?

a)

25

b)

18.75

c)

40.5

d)

50

9.

Michael bought a pair a jeans for $35. What is his total cost after taxes? Current tax is 9%.

a)

$3.15

b)

$38.15

c)

$31.85

d)

$66.50

10.

Decrease $250 by 50%.

a)

175

b)

125

c)

200

d)

300

11.

A store marks up their merchandise by 15% for profit. If the store buys an item for $10 , what will the price of the item be for costumers?

a)

$17.00

b)

$25.00

c)

$8.50

d)

$11.50

12.

Which of the following could be the equation of the exponential function shown graphed below?

a)

$f\left(x\right)=10\left(0.5\right)^x$

b)

$f\left(x\right)=10\left(1.75\right)^x$

c)

$f\left(x\right)=2\left(1.75\right)^x$

d)

$f\left(x\right)=2\left(0.75\right)^x$

13.

The number of bacteria in a lab experiment is increasing by 2.5% per minute. The experiment started with 200 bacteria. How many bacteria, to the nearest whole number, does your model predict will be present after three hours of growth?

a)

17,034

b)

1,525

c)

215

d)

587

14.

Write an equation of an exponential function that passes through the points (0, 4) and (1, 20).

a)

$f\left(x\right)=5\left(4\right)^x$

b)

$f\left(x\right)=5x+4$

c)

$f\left(x\right)=4\left(2\right)^x$

d)

$f\left(x\right)=4\left(5\right)^x$

15.

In a geometric sequence the first term is 5 and the second term is 10, which of the following is the 4th term?

a)

5

b)

10

c)

20

d)

40

16.

$8,\ 4,\ 2,\ 1,\ \frac{1}{2},...$

What is the common ratio of

a)

2

b)

$\frac{1}{2}$

c)

4

d)

$\frac{1}{8}$

17.

A geometric sequence is defined by $a\left(1\right)=3,\ \ \ a\left(n\right)=a\left(n-1\right)\cdot5$ , what is the 4th term of the sequence?

a)

3

b)

5

c)

75

d)

375

18.

The number of visits a day to an amusement park is decreasing. The number of visits can be modeled by the function $h=5124\left(0.25\right)^t$ where h is the number of visits a day and t is the number of days since the decrease started. Which of the following is the average rate of change of h over the interval 2 ≤ t ≤ 4?

a)

$-75$

b)

$-150$

c)

$80$

d)

$-120$

19.

Check all sequences that are geometric.

a)

$4,\ 8,\ 16,\ 32,\ ...$

b)

$10,\ 5,\ \frac{5}{2},\ \frac{5}{4},..$

c)

$4,\ 2,\ 0,\ -2,\ ...$

d)

$1,\ -3,\ 9,\ -27,\ ...$

20.

The table below represents some values of an exponential function. Write the equation of the exponential function in $y=a\left(b\right)^x$ form.

a)

$y=3\left(4\right)^x$

b)

$y=3x+4$

c)

$y=4\left(3\right)^x$

d)

$y=4\left(3\right)x$

Unit 6 Review: Exponents

Total questions: 20

Worksheet time: 20mins

Similar Resources on Wayground