Question 1

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

Accepted Answer

$$81$$

Question 2

What is the result of $$a^0$$ for any nonzero real number $$a$$?

Accepted Answer

$$1$$

Question 3

Simplify the expression $$y^{30}$$ 	imes $$y^{70}$$ using the product rule for exponents.

Accepted Answer

$$y^{100}$$

Question 4

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

Accepted Answer

$$-8$$, negative sign is kept

Question 5

If $$a^m 	imes a^n = a$$^{m+n}$$, what is 4^2$ 	imes 4^1$?

Accepted Answer

$$4^3$$

Question 6

Using the quotient rule, simplify $$4^3$$ / $$4^1.$$

Accepted Answer

$$4^2$$

Question 7

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

Accepted Answer

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

Question 8

A scientist is calculating the concentration of a solution and gets $$x^{-3} as $$part of the formula. How should this be rewritten using positive exponents?

Accepted Answer

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

Question 9

Which statement is true about the exponent rule for dividing terms with the same base?

Accepted Answer

Subtract the exponents: $$a^m / a^n = a$$^{m-n}$$

Question 10

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

Accepted Answer

It is canceled and the result is positive

Question 11

Simplify the following: $$3^4$$ / $$3^2$$

Accepted Answer

$$3^2$$

Question 12

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

Accepted Answer

$$a^n$$

Question 13

A company’s profit function is $$P(x) = 5x$$^{-2}$$. What is P(2$$)$$?

Accepted Answer

$$1.25$$

Question 14

Which of the following is the correct simplification of $$(-4)^2$$?

Accepted Answer

$$16$$

Question 15

If $$a^n is in $$the denominator and $$n is $$negative, how do you rewrite the expression with a positive exponent?

Accepted Answer

$$a^n in $$the numerator

Question 16

A medical dosage formula uses $$d = k t$$^{-1}$$, where k$ is a constant and t$ is time. What does t$$^{-1}$$ mean in this context?

Accepted Answer

$$\frac{1}{t}$$

Question 17

Which of the following is true for $$1^n$$ where $$n is $$any integer?

Accepted Answer

$$1^n = 1$$

Question 18

Simplify $$x^5$$ 	imes $$x^{-2}$$ using exponent rules.

Accepted Answer

$$x^3$$

Question 19

A business analyst models depreciation as $$D(t) = 1000 	imes (0.9)^t. $$What is $$D(0)$$?

Accepted Answer

$$1000$$

Question 20

Which of the following is the correct simplification for $$(-5)^4$$?

Accepted Answer

$$625$$

Rules of Exponents: Essential Properties and Applications

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