Question 1

Which of the following is the correct result for $$(-3)^4$$?

Accepted Answer

$$81$$

Question 2

What is the value of $$1^{100}$$?

Accepted Answer

$$1$$

Question 3

Simplify the expression $$a^5$$ 	imes $$a^3$$ using the product rule for exponents.

Accepted Answer

$$a^{8}$$

Question 4

Evaluate $$(-2)^3$$ and determine if the negative sign is kept or cancelled.

Accepted Answer

$$-8$$, negative sign is kept

Question 5

If $$y^{30}$$ 	imes $$y^{70} is $$simplified, what is the result?

Accepted Answer

$$y^{100}$$

Question 6

Simplify $$\dfrac{4^5$}{4^2$}$$ using the quotient rule for exponents.

Accepted Answer

$$4^3$$

Question 7

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

Accepted Answer

$$1$$

Question 8

A medication’s concentration halves every hour. If the initial concentration is $$C_0$$, what is the concentration after 3 hours?

Accepted Answer

$$C_0$$ \div $$2^3$$

Question 9

Simplify $$\dfrac{1}{a$$^{-4}$$}$$ using the negative exponent rule.

Accepted Answer

$$a^{4}$$

Question 10

Which of the following correctly applies the negative exponent rule to $$2^{-5}$$?

Accepted Answer

$$\dfrac{1}{2^5$}$$

Question 11

A scientist dilutes a solution by a factor of $$10$$ every step. What is the concentration after $$n$$ steps if the initial concentration is $$C_0$$?

Accepted Answer

$$C_0$$ \div 10^n$$

Question 12

Simplify $$(-4)^2$$ and explain the effect of the negative sign.

Accepted Answer

$$16$$, negative sign is cancelled

Question 13

Which rule is used to simplify $$a^m 	imes a^n$$?

Accepted Answer

Product rule: add exponents

Question 14

If $$a^7$$ \div $$a^3 is $$simplified, what is the result?

Accepted Answer

$$a^{4}$$

Question 15

A radioactive substance decays so that its amount halves every day. If the initial amount is $$A_0$$, what is the amount after $$t$$ days?

Accepted Answer

$$A_0$$ \div 2^t$$

Question 16

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

Accepted Answer

$$a^{7}$$

Question 17

Which of the following is equivalent to $$x^{-3}$$?

Accepted Answer

$$\dfrac{1}{x^3$}$$

Question 18

If $$(-a)^{even} is $$simplified, what happens to the negative sign?

Accepted Answer

It is cancelled

Question 19

Which of the following is the correct simplification for $$\dfrac{1}{b$$^{-6}$$}$$?

Accepted Answer

$$b^{6}$$

Question 20

A population triples every year. If the initial population is $$P_0$$, what is the population after $$n$$ years?

Accepted Answer

$$P_0$$ 	imes 3^n$$

Rules of Exponents: Essential Properties and Applications

Study Guide - Practice Questions