Q: Which of the following is the correct application of the zero exponent rule?

$$a^0 = 1$ for any a$$ \neq 0$$

Question 1

Which of the following correctly applies the power rule to simplify $$\left( x^3$ \$$right)^4$$?

Accepted Answer

$$x^{12}$$

Question 2

Simplify the expression $$\dfrac{5^7$}{5^3$}$$ using the properties of exponents.

Accepted Answer

$$5^4$$

Question 3

Which of the following is equivalent to $$\dfrac{a$$^{-3}$$b^2$$}{$$a^2b$$^{-4}$$}$$ with positive exponents?

Accepted Answer

$$\dfrac{b^6$}{a^5$}$$

Question 4

If $$x^{-2} = 16$, what is the value of x$?

Accepted Answer

$$\dfrac{1}{4}$$

Question 5

Which property of exponents justifies the step $$b^m \cdot b^n = b$$^{m+n}$$?

Accepted Answer

Product Rule

Question 6

Simplify $$\left( \dfrac{2x^3$}{y^2$} \$$right)^2$$.

Accepted Answer

$$\dfrac{4x^6$}{y^4$}$$

Question 7

Which of the following is equivalent to $$\sqrt[3]{x^6$}$$?

Accepted Answer

$$x^2$$

Question 8

A biologist is studying bacteria growth modeled by $$N = 2^t$$, where $$t is $$time in hours. If the population after 3 hours is $$N = 2^3$, what is the population?

Accepted Answer

$$8$$

Question 9

Simplify $$\dfrac{(3x^2$y^{-1})^3$}{9x^3$y^{-2}$$}$ and write your answer with positive exponents.

Accepted Answer

$$x^3y^3$

Question 10

Which of the following is the correct application of the zero exponent rule?

Accepted Answer

$$a^0 = 1$ for any a$$ 
eq 0$$

Question 11

Simplify $$\left( \dfrac{a^2$b^{-3}$$}{$$a^{-1}b^2$} \$$right)^2$$.

Accepted Answer

$$a^6b$$^{-10}$

Question 12

Which of the following is equivalent to $$\dfrac{1}{x$$^{-5}$$}$$?

Accepted Answer

$$x^5$$

Question 13

A chemist dilutes a solution so that its concentration halves every hour. If the initial concentration is $$C_0$$, which expression gives the concentration after $$t$$ hours?

Accepted Answer

$$C_0$$ \cdot (\dfrac{1}{2})^t$$

Question 14

Simplify $$\left( x$$^{-2}$$y^3$$ \$$right)^2$ and write your answer with positive exponents.

Accepted Answer

$$\dfrac{y^6$}{x^4$}$$

Question 15

Which of the following is equivalent to $$\sqrt[4]{x^8$}$$?

Accepted Answer

$$x^2$$

Question 16

If $$a^x = a^y$$ and $$a 
eq 0$$, what must be true?

Accepted Answer

$$x = y$$

Question 17

Simplify $$\dfrac{(2x$$^{-1}$$y^2)^3$}{4x^2$y^{-1}$$}$ and write your answer with positive exponents.

Accepted Answer

Question 18

Which of the following is the correct application of the negative exponent rule?

Accepted Answer

$$a^{-n}$$ = \dfrac{1}{a^n}$$

Question 19

Simplify $$\left( \dfrac{3x^2$}{y^3$} \$$right)^2$$.

Accepted Answer

$$\dfrac{9x^4$}{y^6$}$$

C1

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