Powers of Monomials

Laws of Exponents Review

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We've already studied the following exponent laws and rules:

• When you multiply two monomials, multiply the coefficient and add the exponents.

• When you divide two monomials, divide the coefficient and subtract the exponents.

• When you take the power of a monomial, take the power of the coefficient and multiply the exponents by the power.

• Get rid of negative exponents by moving them, along with their base, to the opposite side of the fraction bar.

Let's review these laws one at a time...

When you multiply two monomials, multiply the coefficient and add the exponents.

Multiple Choice

$$9x^6y^2\cdot5x^2y^3$$  

• $$14x^8y^5$$  

• $$14x^{12}y^6$$  

• $$45x^8y^5$$  

• $$45x^{12}y^6$$  

• $$45x^8y^6$$  

Multiple Choice

Simplify (-4r⁵)(2r⁸)

• -8r¹³
• -2r¹³
• -8r⁴⁰
• -2y⁴⁰

When you divide monomials, divide the coefficients and subtract the exponents.

Multiple Choice

• 8x⁴
• 8x⁸
• 6x⁴
• 6x⁸

Multiple Choice

Simplify the expression.

• 1/y⁵
• 1/y²
• y²
• y⁵

Multiple Choice

$$\frac{8x^2y^3}{2xy^3}$$  

• $$\frac{x}{2}$$  

• $$4x$$  

• $$4xy$$  

• 0

When you take the power of a monomial, take the power of the coefficient and multiply the exponents by the power

Multiple Choice

 Simplify
(3x³y⁵)⁴

• 3x¹²y²⁰
• 81x¹²y²⁰
• 12x¹²y²⁰
• 81x⁷y⁹

Multiple Choice

(5²)³

• 5⁶

• 5⁵

• 5⁷

• 5⁸

Multiple Choice

(5²)³

• 5⁶
• 5⁵
• 5⁷
• 5⁸

Get rid of negative exponents by moving them, along with their base, to the opposite side of the fraction bar.

Multiple Choice

Simplify: $$\frac{x^2y^5}{x^9y^5}$$  

• $$x^2$$  

• $$\frac{1}{x^2}$$  

• $$\frac{1}{x^7}$$  

• $$x^7$$  

Multiple Choice

Which expression is equivalent to $$\frac{x^2y^2z^2}{4y^4}$$ ?

• $$4y^6$$  

• $$y^6$$  

• $$\frac{x^2z^2}{4y^2}$$  

• $$4x^2y^6z^2$$  

Multiple Choice

Rewrite using a positive exponent.

7^-10

• ¹/₇¹⁰

• 7¹⁰

• ¹/₇^-10

• -70

Multiple Choice

Rewrite using a positive exponent.

7^-10

• ¹/₇¹⁰

• 7¹⁰

• ¹/₇^-10

• -70