Question 1

Which of the following correctly applies the product rule for exponents to simplify $$x^3$$ \cdot $$x^5$$?

Accepted Answer

$$x^{8}$$

Question 2

What is the value of $$7^0$$?

Accepted Answer

$$1$$

Question 3

Simplify the expression $$\dfrac{a^7$}{a^3$}$$ using the quotient rule for exponents.

Accepted Answer

$$a^{4}$$

Question 4

Which of the following is equivalent to $$x^{-4}$$, written with positive exponents only?

Accepted Answer

$$\dfrac{1}{x^4$}$$

Question 5

Convert $$0.00052 to $$scientific notation.

Accepted Answer

$$5.2 	imes 10$$^{-4}$$

Question 6

Write $$3.6 	imes 10^5$ in standard notation.

Accepted Answer

$$360,000$$

Question 7

Simplify the expression $$\$$left(2x^3$$y^2$$\$$right)^2$.

Accepted Answer

$$4x^6y^4$

Question 8

Which of the following is the correct simplification of $$\dfrac{5x$$^{-2}$$}{x^3$}$$?

Accepted Answer

$$5x^{-5}$$

Question 9

A chemist measures a sample with a mass of $$4.2 	imes 10$$^{-3}$$ grams. What is this mass in standard notation?

Accepted Answer

$$0.0042$$ grams

Question 10

Simplify $$\dfrac{(3a^2$b^{-3})^2$}{a$$^{-1}$$b^4$$}$ and write with positive exponents only.

Accepted Answer

$$\dfrac{9a^5$}{b$$^{10}$$}$$

Question 11

Which of the following is the correct application of the zero exponent rule to $$(-5x^2y^3$)^0$$?

Accepted Answer

$$1$$

Question 12

A medical researcher records a virus concentration as $$2.5 	imes 10^6$ particles per mL. What is this value in standard notation?

Accepted Answer

$$2,500,000$$ particles/mL

Question 13

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

Accepted Answer

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

Question 14

Which of the following is the correct simplification of $$\dfrac{(x^2$y^{-1})^3$}{x$$^{-4}$$y^2$$}$?

Accepted Answer

Question 15

A city’s population is $$1.2 	imes 10^7$. What is this number in standard notation?

Accepted Answer

$$12,000,000$$

Question 16

Simplify $$\dfrac{4x^0$y^{-2}$$}{$$2x^{-3}y$$}$ and write with positive exponents only.

Accepted Answer

$$2x^3y$$^{-3}$

Question 17

Which of the following is the correct simplification of $$\left(\dfrac{3x$$^{-2}$$}{y^3$}\$$right)^{-1}$$?

Accepted Answer

$$\dfrac{x^2$}{3y^3$}$$

Question 18

Convert $$8,900,000 to $$scientific notation.

Accepted Answer

$$8.9 	imes 10^6$

Question 19

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

Accepted Answer

$$-8x^6y$$^{-9}$

Question 20

A scientist records a measurement as $$6.1 	imes 10$$^{-7}$$ meters. What is this value in standard notation?

Accepted Answer

$$0.00000061$$ meters

Exponents, Polynomials, and Scientific Notation – Core Concepts and Rules

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