Question 1

Which of the following is the correct value of $$(-4)^6$$?

Accepted Answer

$$4096$$

Question 2

Evaluate $$(-5)^3$$ and select the correct answer.

Accepted Answer

$$-125$$

Question 3

Simplify the expression $$x^7$$ 	imes $$x^3$$ using the product rule for exponents.

Accepted Answer

$$x^{10}$$

Question 4

Which of the following correctly applies the quotient rule to $$\dfrac{y^9$}{y^4$}$$?

Accepted Answer

$$y^{5}$$

Question 5

What is the value of $$a^0$$ for any nonzero $$a$$?

Accepted Answer

$$1$$

Question 6

Simplify $$\dfrac{2^7$}{2^3$}$$ using exponent rules.

Accepted Answer

$$2^{4}$$

Question 7

A scientist is calculating the concentration of a solution and needs to simplify $$\dfrac{c$$^{-2}$$}{c^5$}. $$What is the result?

Accepted Answer

$$c^{-7}$$

Question 8

Which of the following is equivalent to $$\dfrac{1}{a$$^{-4}$$}$$?

Accepted Answer

$$a^{4}$$

Question 9

A medical researcher is analyzing exponential growth and writes $$(-2)^{10}. $$What is the sign of the result?

Accepted Answer

Positive

Question 10

Simplify the following expression: $$\dfrac{5^3$ 	imes 5^2$}{5^4$}$$

Accepted Answer

$$5^{1}$$

Question 11

Which of the following is the correct simplification of $$\dfrac{1}{x$$^{-7}$$}$$?

Accepted Answer

$$x^{7}$$

Question 12

If $$a is a $$nonzero real number, which of the following is equivalent to $$a^{-n}$$?

Accepted Answer

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

Question 13

A chemist doubles the concentration of a reactant, represented as $$c^2. If $$the concentration is halved, what exponent should be used?

Accepted Answer

$$c^{-1}$$

Question 14

Simplify $$(-3)^4$$ and choose the correct answer.

Accepted Answer

$$81$$

Question 15

Which of the following is the correct application of the product rule for exponents to $$y^{12}$$ 	imes $$y^{8}$$?

Accepted Answer

$$y^{20}$$

Question 16

A biologist is studying population growth modeled by $$P(t) = P_0$ 	imes 2$$^{t}$$. If the population doubles every year, what is P(3$$)$$ in terms of P_0$?

Accepted Answer

$$8P_0$$

Question 17

Simplify $$\dfrac{4^5$}{4^2$}$$ using exponent rules.

Accepted Answer

$$4^{3}$$

Question 18

Which of the following is the correct simplification of $$a^3$$ 	imes $$a^{-2}$$?

Accepted Answer

$$a^{1}$$

Question 19

A physicist is working with the formula $$E = mc^2$. If c$ is replaced by c$$^{-1}$$, what is the new formula for E$?

Accepted Answer

$$E = m c$$^{-2}$$

Question 20

Which of the following is the correct simplification of $$\dfrac{1}{2$$^{-3}$$}$$?

Accepted Answer

$$2^{3}$$

Rules of Exponents: Essential Properties and Applications

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