Question 1

Which of the following correctly applies the Product Rule to simplify $$x^3$$ \cdot $$x^7$$?

Accepted Answer

$$x^{10}$$

Question 2

Simplify the expression $$\dfrac{a^8$}{a^3$}$$ using the Quotient Rule.

Accepted Answer

$$a^5$$

Question 3

Which of the following is equivalent to $$(2x^3y^2$)^4$$ using the Power of a Product Rule?

Accepted Answer

$$16x^{12}y^8$

Question 4

What is the value of $$17^0$$ according to the Zero Exponent Rule?

Accepted Answer

$$1$$

Question 5

Simplify $$\dfrac{2x^7$y^3$$}{$$4x^2y^5$}$$ and write your answer using only positive exponents.

Accepted Answer

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

Question 6

Which of the following is the correct scientific notation for the number 12,400,000,000,000?

Accepted Answer

$$1.24 	imes 10$$^{13}$$

Question 7

A cylinder has a volume given by $$V = \pi r^2$ h. If $$the radius is $$3 ft $$and the height is $$5 ft$$, what is the volume in terms of $$\pi$$?

Accepted Answer

$$45\pi ft$^3$$

Question 8

Which of the following is equivalent to $$4^{-3}$$ using the Negative Exponent Rule?

Accepted Answer

$$\dfrac{1}{4^3$}$$

Question 9

Multiply $$(1.2 	imes 10^4$) \cdot (1.3 	imes 10^6$)$$ and write your answer in scientific notation.

Accepted Answer

$$1.56 	imes 10$$^{10}$$

Question 10

If $$a^m \cdot a^n = a$$^{m+n}$$, which property of exponents does this represent?

Accepted Answer

Product Rule

Question 11

Simplify $$\left(\dfrac{3x^4$}{y^2$}\$$right)^3$$ using the Power of a Quotient Rule.

Accepted Answer

$$\dfrac{27x$$^{12}$$}{y^6$}$$

Question 12

Which of the following is the correct standard form for $$2.4 	imes 10^5$?

Accepted Answer

$$240,000$$

Question 13

A savings account grows from $$100 to$$ $$121 in$$ $$4$$ years at compounded annual interest. What is the annual interest rate?

Accepted Answer

$$5\%$$

Question 14

Which of the following is equivalent to $$(-2)^7$$ \cdot $$(-2)^3$$?

Accepted Answer

$$(-2)^{10}$$

Question 15

Simplify $$\dfrac{18x^5$y^{-4}$$}{$$12x^2y^7$}$$ and write your answer using only positive exponents.

Accepted Answer

$$\dfrac{3x^3$}{2y$$^{11}$$}$$

Question 16

Which of the following is the correct application of the Power Rule to $$(a^2)^5$?

Accepted Answer

$$a^{10}$$

Question 17

If the surface area of a rectangular solid is $$S = 2lw + 2lh + 2wh$$, what is the surface area when $$l = 2$$, $$w = 3$$, and $$h = 4$$?

Accepted Answer

$$52$$

Question 18

Which of the following is the correct scientific notation for the number $$0.0000054$$?

Accepted Answer

$$5.4 	imes 10$$^{-6}$$

Question 19

Simplify $$\dfrac{x^7$y^2$$}{$$x^3y^5$}$$ and write your answer using only positive exponents.

Accepted Answer

$$x^4y$$^{-3}$

Question 20

Which of the following is the correct application of the Negative Exponent Rule to $$\left(\dfrac{4}{5}\$$right)^{-2}$$?

Accepted Answer

$$\left(\dfrac{5}{4}\$$right)^2$$

Rules of Exponents and Applications: College Algebra Study Notes

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