Free Printable Unit 2: Retest #1

1.

A circle has a radius of $3x^6y^8$ cm. The area of a circle can be found using $A=\pi r^2$ . What is the area of the circle in square centimeters?

a)

$9\pi x^8y^{10}\ cm^2$

b)

$6\pi x^8y^{10}\ cm^2$

c)

$6\pi x^{12}y^{16}\ cm^2$

d)

$9\pi x^{12}y^{16}\ cm^2$

2.

a)

$4x^3$

b)

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

c)

$3x^4$

d)

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

3.

Which of the following is equivalent to $x^{-7}$ ?

a)

$None\ of\ the\ above$

b)

$x^7$

c)

$\frac{1}{x^{-7}}$

d)

$\frac{1}{x^7}$

4.

Which expression is equivalent to $\frac{20b^8i^5}{2i^2}\cdot\frac{5\left(b^7\right)^4}{i^5}$ for all values of $b$ and $i$ where the expression is defined.

a)

$50b^{36}i^8$

b)

$\frac{50b^{36}}{i^2}$

c)

$\frac{90b^{20}}{i^2}$

d)

$90b^{20}i^8$

5.

Which expression is equivalent to $\left(3x^5\right)^2\left(x^{10}\right)^{\frac{1}{2}}$ ?

a)

$6x^{10}$

b)

$6x^{15}$

c)

$9x^{15}$

d)

$9x^{10}$

6.

Which expression is equivalent to $\left(9k^{16}v^{20}\right)^{\frac{1}{2}}$ for all positive values of $k$ and $v$ ?

a)

$9k^8v^{10}$

b)

$3k^{16}v^{20}$

c)

$4.5k^{16}v^{20}$

d)

$3k^8v^{10}$

7.

Simplify: $\left(2xy^4\right)\left(5x^3y^4z\right)$

a)

$10x^3y^{16}z$

b)

$7x^3y^{16}$

c)

$7x^4y^8z$

d)

$10x^4y^8z$

8.

$\frac{\left(x^3\right)^3\cdot x}{x^6}$ is equivalent to $x^n$ . What is the value of $n$ ?

a)

4

b)

5

c)

6

d)

3

9.

Which expression is equivalent to $\frac{-14x^{-1}y^4z^{-3}}{2x^{-2}yz^5}$ ?

a)

$\frac{-7y^5z^2}{x^3}$

b)

$\frac{-7y^3}{x^3z^8}$

c)

$-7xy^3z^8$

d)

$\frac{-7xy^3}{z^8}$

10.

What is the value of the following expression $\left(\frac{5^{-2}a^3}{b^{-1}}\right)^{^0}$ ?

a)

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

b)

$1$

c)

$25a^2b$

d)

$0$

11.

Which expression is equivalent to $\frac{34a^6b^9c^{-4}}{6a^{-5}b^5c^{-2}}$ ?

a)

$\frac{17a^{11}b^4}{3c^2}$

b)

$\frac{17a^1b^4}{3c^6}$

c)

$\frac{28a^1b^{14}}{c^6}$

d)

$\frac{17b^1c^2}{3a^1}$

12.

Find the volume of a rectangular prism whose dimensions are $3x^{7\ },\ \ 5x^3y^3\ ,\ \ and\ \ 4x^2y^4$ . $\left[V=lwh\right]$

a)

$60x^{42}y^{12}$

b)

$15x^{12}y^7$

c)

$20x^{12}y^7$

d)

$60x^{12}y^7$

13.

A cube has a side length of $5x^2y^3z^5$ cm. The volume can be found using $v=s^3$ . What is the volume of this cube in cubic centimeters?

a)

$15x^5y^6z^8$

b)

$15x^6y^9z^{15}$

c)

$125x^6y^9z^{15}$

d)

$125x^5y^6z^8$

14.

Simplify: $k^{-4}\cdot y^6\cdot k^4$

a)

$\frac{y^6}{k^8}$

b)

$k\cdot y^6$

c)

$y^6$

d)

$\frac{1}{k^8y^6}$

15.

Which expression is equivalent to $\frac{\left(d^2\right)^{-4}}{d^{-17}}$ for all values of $d$ where the expression is defined?

a)

$d^{25}$

b)

$\frac{1}{d^9}$

c)

$d^9$

d)

$\frac{1}{d^{25}}$

16.

$\left(h^2\right)\left(h^{-12}\right)$ is equivalent to $h^n$ . What is the value of $n$ ?

(a)

17.

The area of a rectangle is $12c^{32}k^{24}$ square yards. If the length of the rectangle is $4c^8k^8$ yards, which expression represents the width of the rectangle in yards?

a)

$16c^{40}k^{32}$

b)

$3c^4k^3$

c)

$8c^{24}k^{16}$

d)

$3c^{24}k^{16}$

Unit 2: Retest #1 - Laws of Exponents

Total questions: 17

Worksheet time: 51mins

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