Question 1

Which of the following correctly applies the product rule for exponents to simplify $$5a^3$$ \cdot $$3a^4$$?

Accepted Answer

$$15a^7$$

Question 2

What is the value of $$(4m)^0$$?

Accepted Answer

$$1$$

Question 3

Simplify the expression $$\left(\dfrac{3x^4$}{y^3$}\$$right)^3$$ using the properties of exponents.

Accepted Answer

$$\dfrac{27x$$^{12}$$}{y^9$}$$

Question 4

Which of the following is equivalent to $$a^5$$ \cdot $$a^2$$?

Accepted Answer

$$a^7$$

Question 5

Simplify $$(x^5)^2$ using the power rule for exponents.

Accepted Answer

$$x^{10}$$

Question 6

Which of the following is the correct application of the quotient rule for exponents: $$\dfrac{4p^5$q^7$$}{$$6p^2q$$}$?

Accepted Answer

$$\dfrac{2p^3$q^6$$}{3}$

Question 7

Evaluate $$-4x^{-3}$$ and express your answer using only positive exponents.

Accepted Answer

$$-\dfrac{4}{x^3$}$$

Question 8

Convert $$0.00032 to $$scientific notation.

Accepted Answer

$$3.2 	imes 10$$^{-4}$$

Question 9

Which of the following expressions is NOT a polynomial?

Accepted Answer

$$-3a^{-4}$$

Question 10

Given the polynomial $$4x^2$$ - $$6x^3 - 7 + 8x$, what is the leading term when written in descending order?

Accepted Answer

$$-6x^3$$

Question 11

Combine like terms and write in descending order: $$6m + 4m^2$ - 10m + 12m^2$ + 3.$$

Accepted Answer

$$16m^2 - 4m + 3$

Question 12

Evaluate the polynomial $$-3x^2 - 4x + 2$ for x = -2$.

Accepted Answer

$$-2$$

Question 13

Simplify $$(2x - 5) + (4 - 3x) - (-5x + 8).$$

Accepted Answer

$$4x + 7$$

Question 14

A rectangle has a length of $$x$$ feet and a width of $$(3x - 1)$$ feet. Write a simplified polynomial that represents the perimeter of the rectangle.

Accepted Answer

$$8x - 2$$

Question 15

Multiply $$(3a^2)(-a$$)$$.

Accepted Answer

$$-3a^3$$

Question 16

Multiply $$(4x - 3)(x - 2).$$

Accepted Answer

$$4x^2 - 11x + 6$

Question 17

If a square has a side length of $$6x$$ and another square has a side length of $$x$$, what is the total area of the two squares?

Accepted Answer

$$37x^2$$

Question 18

Evaluate the polynomial $$3x + xy^2$ + 8x^2$ for x = -2$ and y = 5$.

Accepted Answer

$$66$$

Question 19

Which of the following pairs are like terms?

Accepted Answer

$$3a^3b^2$ and $$-\dfrac{1}{2}$$b^2a^3$

Exponents and Polynomials: Properties, Operations, and Applications

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