Question 1

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

Accepted Answer

$$a^{8}$$

Question 2

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

Accepted Answer

$$m^{4}$$

Question 3

What is the result of $$(-2x^3)^2$?

Accepted Answer

$$4x^6$$

Question 4

Which of the following is equivalent to $$a^{-4}$$?

Accepted Answer

$$\frac{1}{a^4$}$$

Question 5

Express $$\frac{2x$$^{-3}$$y^2$$}{$$4y^{-1}x$$}$ with only positive exponents and simplify.

Accepted Answer

$$\frac{y^3$}{2x^4$}$$

Question 6

Write $$0.00037 in $$scientific notation.

Accepted Answer

$$3.7 	imes 10$$^{-4}$$

Question 7

Multiply and simplify: $$(2.5 	imes 10^3$) 	imes (4 	imes 10^5$).$$

Accepted Answer

$$1.0 	imes 10^7$

Question 8

Divide and simplify: $$\frac{9.6 	imes 10^8$}{3.2 	imes 10^4$}.$$

Accepted Answer

$$3 	imes 10^5$

Question 9

Which of the following is a binomial?

Accepted Answer

$$x^2 + 2x$

Question 10

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

Accepted Answer

$$3$$

Question 11

Combine like terms: $$5x^2 + 3x$$ - $$2x^2 + 7$.

Accepted Answer

$$3x^2 + 3x + 7$

Question 12

Evaluate the polynomial $$-x^2 + 3x + 9$ for x = -2$.

Accepted Answer

$$1$$

Question 13

A square city park has side length $$x$$ feet. A circular fountain of diameter $$4$$ feet is built in the center. Write a polynomial for the remaining area of the park.

Accepted Answer

$$x^2 - 4$$\pi$$

Question 14

Multiply and simplify: $$(2x^2)(3x^3$)$.

Accepted Answer

$$6x^5$$

Question 15

Subtract the polynomials: $$(5x^2 + 3x$$) - $$(2x^2 - x$$)$$.

Accepted Answer

$$3x^2 + 4x$

Question 16

Which of the following is the correct result of $$\left(\frac{a^2$b^3$$}{$$c^4$$}\$$right)^2$?

Accepted Answer

$$\frac{a^4$b^6$$}{$$c^8$$}$

Question 17

A wind turbine generates power $$P (in $$watts) at a wind speed $$v (in $$mph) according to $$P = 0.0571v^3$. What is the power generated when v = 20$ mph?

Accepted Answer

$$228.4$$ watts

Question 18

Which of the following is the leading term of the polynomial $$6x^4$$ - $$2x^3 + 5x - 1$?

Accepted Answer

$$6x^4$$

Question 19

Simplify $$\left(\frac{2x$$^{-2}$$y^3$$}{$$4y^{-1}x^2$}\right)$$ using only positive exponents.

Accepted Answer

$$\frac{y^4$}{2x^4$}$$

Exponents and Polynomials: Structured Study Notes for Beginning Algebra

Study Guide - Practice Questions

Study Guide - Flashcards