Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

$$4x^6/y^4$

Question 3

Which of the following is the correct application of the zero-exponent rule for any nonzero real number $$a$$?

Accepted Answer

$$a^0 = 1$

Question 4

Simplify the following using the product rule: $$x^4$$ \cdot $$x^7$$

Accepted Answer

$$x^{11}$$

Question 5

Which of the following expressions is equivalent to $$\$$left(a^2$$b^3$$\$$right)^4$?

Accepted Answer

$$a^8b$$^{12}$

Question 6

Simplify the following using the quotient rule: $$\dfrac{y^9$}{y^4$}$$

Accepted Answer

$$y^{5}$$

Question 7

Which of the following is the correct application of the products-to-powers rule for $$(3x)^5$$?

Accepted Answer

$$3^5x^5$

Question 8

Simplify the following using the quotients-to-powers rule: $$\left(\dfrac{2x}{y^2$}\$$right)^3$$

Accepted Answer

$$\dfrac{8x^3$}{y^6$}$$

Question 9

Which of the following is written in proper scientific notation?

Accepted Answer

$$5.2 	imes 10^5$

Question 10

Convert $$0.00047 to $$scientific notation.

Accepted Answer

$$4.7 	imes 10$$^{-3}$$

Question 11

A typical red blood cell has a diameter of about $$7.2 	imes 10$$^{-6}$$ meters. What is this value in decimal notation?

Accepted Answer

$$0.0000072$$

Question 12

Simplify and write your answer in scientific notation: $$(3.0 	imes 10^4$) 	imes (2.0 	imes 10^3$)$$

Accepted Answer

$$6.0 	imes 10^6$

Question 13

A computer processor can perform $$2.5 	imes 10^9$ operations per second. How many operations can it perform in 4$$ 	imes $$10^2$$ seconds? Express your answer in scientific notation.

Accepted Answer

$$1.0 	imes 10$$^{12}$$

Question 14

Simplify the following expression and write your answer with only positive exponents: $$\dfrac{2x$$^{-3}$$y^2$$}{$$4x^2y$$^{-4}$$}$$

Accepted Answer

$$\dfrac{y^6$}{2x^5$}$$

Question 15

Which of the following is NOT a requirement for an exponential expression to be considered simplified?

Accepted Answer

The exponents must all be even numbers.

Question 16

A scientist measures the mass of a virus particle as $$3.2 	imes 10$$^{-18}$$ grams. Which of the following is the correct decimal notation?

Accepted Answer

$$0.0000000000000000032$$

Question 17

Simplify the following expression: $$\dfrac{(2x^2$y^{-3})^2$}{4x$$^{-2}$$y}$$

Accepted Answer

$$x^6/y^7$

Question 18

Which of the following is the correct result of $$(5.0 	imes 10^6$) \div (2.0 	imes 10^2$) in $$scientific notation?

Accepted Answer

$$2.5 	imes 10^4$

Exponents and Scientific Notation: Fundamental Concepts of Algebra (Precalculus Chapter P.2)

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