Exponents Review

Match

Match the following terms with their simplified forms.

• $$x^1$$

• $$y^0$$  

• $$xyz^0$$  

• $$xyz^1$$  

• $$0^1$$  

x

1

xy

xyz

0

• x

• 1

• xy

• xyz

• 0

Multiple Choice

$$\left(5x^2y^4\right)^3$$  

• $$125x^6y^{12}$$  

• $$15x^6y^{12}$$  

• $$8x^5y^7$$  

• $$15x^5y^7$$  

Multiple Choice

$$\frac{\left(2m^3n^2\right)^02m^3n^{-3}}{n^3}$$  

Simplify so there are no negative exponents in the answer.

• $$\frac{2m^3}{n^{6^{ }}}$$  

• $$2m^3$$  

• $$4m^6n^2$$  

• $$2m^6n^2$$  

Multiple Choice

Simplify so there are no negative exponents in the answer.

$$\left(3n^3\right)^{-3}$$  

• $$\frac{1}{27n^9}$$  

• $$\frac{-27}{n^9}$$  

• $$\frac{-27}{n^6}$$  

• $$\frac{-9}{n^6}$$  

Multiple Choice

$$3^{3\ }\ ,\ \ \ 5^{-3\ \ },\ \ \left(-6\right)^2\ \ ,\ \ -4^3$$  What is the correct order from least to greatest?

• $$5^{-3\ \ },\ -4^3\ ,\ \ 3^3\ \ ,\ \left(-6\right)^2$$  

• $$-4^{3\ }\ ,\ \ 5^{-3\ },\ 3^3\ ,\ \left(-6\right)^2$$  

• $$\left(-6\right)^{2\ },\ 5^{-3}\ ,\ -4^{3\ },\ 3^3$$  

• $$3^{3\ }\ ,\ \ \ 5^{-3\ \ },\ \ \left(-6\right)^2\ \ ,\ \ -4^3$$  

Multiple Choice

$$\frac{3^3}{3^{-5}}\ =\ 3^{-2}$$ Austin solved the problem to the left. Is he right? Explain your answer.

• Austin is right because when dividing in exponential notation you can subtract the exponents and 3-5 = -2.

• Austin is incorrect because when dividing in exponential notation you can subtract the exponents and 3 - -5 = 8. Therefore his answer should be 3^8.

• Austin is incorrect because he needed to write his final answer as a positive exponent. The answer should be 1/3^2.

• None of the above.

Multiple Choice

$$\left(\frac{-8p^{10}}{7r^3}\right)^{^2}$$ Simplify.

• -64p²⁰/ 49r⁶

• 64p²⁰/ 49r⁶

• -8p²⁰/ 14r⁶

• -64p¹²/ 49r⁵

Multiple Choice

Combine like terms $$7p^2-5p^3+6p^3+4p^4-9p^2$$  

• $$4p^4+p^3-2p^2$$  

• $$4p^4+p^6-2p^4$$  

• $$4p^4+p^3+2p^2$$  

• $$3p^{14}$$  

Multiple Choice

$$b^3\cdot b^4\cdot b^7\cdot b$$  

• $$b^{15}$$  

• $$b^{14}$$  

• $$b^{84}$$  

• $$b^{49}$$  

Multiple Select

Will the product of (-14)⁴ be positive or negative and why? (select both the answer and the explanation)

• Positive

• Negative

• Because negative base with an even exponent is always positive

• Because negative base with an odd exponent is always negative

Multiple Choice

$$\frac{9a^3b^5}{-3ab^2}$$  

• $$-3a^2b^3$$  

• $$6a^2b^3$$  

• $$3a^3b^3$$  

• $$-\frac{1}{3}a^2b^3$$  

Multiple Choice

$$7^0$$  

• 1

• 7

• 0

• 70

Multiple Choice

$$\frac{xy^7}{x^3y^4}$$  

• $$\frac{y^3}{x^2}$$  

• $$x^2y^3$$  

• $$\frac{x^2}{y^3}$$  

• $$\frac{y^3}{x^3}$$  

Multiple Choice

$$\left(7xy\right)^2$$  

• $$49x^2y^2$$  

• $$14x^2y^2$$  

• $$49x^3y^3$$  

• $$14x^3y^3$$  

Multiple Choice

$$\left(6x^2\right)\left(3x^{-5}\right)$$  

• $$\frac{18}{x^{10}}$$  

• $$18x^3$$  

• $$\frac{18}{x^3}$$  

• $$\frac{1}{18x^3}$$  

Multiple Choice

$$8x^0$$  

• 8

• 1

• 0

• x

Multiple Choice

$$\left(\frac{3m^2n^7}{m}\right)^5$$  

• $$243m^5n^{35}$$  

• $$15m^{10}n^{35}$$  

• $$\frac{243n^{35}}{m^5}$$  

• $$15m^5n^{35}$$  

Multiple Choice

$$6x^5\cdot3x^5\cdot x^0$$  

• $$18x^{10}$$  

• $$9x^{10}$$  

• $$18x^{25}$$  

• $$9x^{25}$$