Question 1

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

Accepted Answer

$$x^8$$

Question 2

Simplify the expression $$\$$left(2x^3$$y^2$$\$$right)^4$ using the power of a product rule.

Accepted Answer

$$2^4x$$^{12}$$y^8$$

Question 3

What is the result of $$\dfrac{x^7$}{x^3$}$$ using the quotient rule for exponents?

Accepted Answer

$$x^{4}$$

Question 4

Which of the following is equivalent to $$\$$left(a^2$$b^3$$\$$right)^5$?

Accepted Answer

$$a^{10}b$$^{15}$

Question 5

Simplify $$\dfrac{2x$$^{-3}$$y^4$$}{$$4x^2y$$^{-1}$$}$$ and write your answer with only positive exponents.

Accepted Answer

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

Question 6

What is the simplified form of $$\left(\dfrac{a^3$b^{-2}$$}{$$a^{-1}b^4$}\$$right)^2$$?

Accepted Answer

Question 7

If $$x^0y^5$z^2 is $$simplified, what is the result?

Accepted Answer

$$y^5z^2$

Question 8

Which of the following is the correct application of the negative exponent rule to $$x^{-4}$$?

Accepted Answer

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

Question 9

Simplify $$\$$left(3x^2$$y^{-1}$$\$$right)^3$ and write your answer with only positive exponents.

Accepted Answer

$$27x^6$$\dfrac{1}{$$y^3$$}$$

Question 10

Which of the following expressions is equivalent to $$\dfrac{a^5$b^{-2}$$}{$$a^{-3}b^4$}$$?

Accepted Answer

$$a^8b$$^{-6}$

Question 11

A chemist is mixing two solutions, one with concentration $$x^2$$ and another with $$x^3. $$What is the total concentration if the solutions are combined?

Accepted Answer

$$x^2$$ + $$x^3$$

Question 12

Simplify the polynomial $$2x^2 + 4x$$ - $$5x^2 + 7$.

Accepted Answer

$$-3x^2 + 4x + 7$

Question 13

What is the degree of the polynomial $$4x^3y^2$ - 2x^2$y^4 + 7$?

Accepted Answer

$$6$$

Question 14

Which of the following is the result of multiplying $$(x^2 - 3x + 1$$)$$ by (2x - 5$$)$$?

Accepted Answer

$$2x^3$$ - $$11x^2 + 13x - 5$

Question 15

A biologist is studying population growth modeled by $$P(t) = 2^t. If $$the population doubles every year, what is $$P(3)$$?

Accepted Answer

$$8$$

Question 16

Simplify $$\left(\dfrac{x^2$y^{-3}$$}{$$x^{-1}y^4$}\$$right)^2$$ and write your answer with only positive exponents.

Accepted Answer

Question 17

Which of the following is the correct result of $$\$$left(2x^3$$y^2$$\$$right)^2$$ \div \$$left(4x^2y^5$\right)$$?

Accepted Answer

Question 18

A medical researcher is analyzing the rate of decay of a drug modeled by $$C(t) = C_0$ \cdot 0.5^t. $$What is the concentration after 4 hours if $$C_0 = 32$ mg?

Accepted Answer

$$2 mg$$

Question 19

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

Accepted Answer

Exponent Rules and Polynomials: Precalculus Study Notes

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