Powers of Monomials

Monomials & Properties of Exponents

Product of Powers

Add the exponents of like bases to find the product of powers.

Open Ended

Simplify 3² x 3⁵.

Open Ended

Simplify 7⁸ x 7⁴.

Multiplying Exponents with Like Bases

• STEP 1: Group terms with like bases.

• STEP 2: Add the exponents of powers with like bases.

q³ x r² x q⁶

STEP 1: q³ x q⁶ x r²

STEP2: q^{(3 + 6)} x r² = q⁹r²

Open Ended

Simplify a²b⁶a⁴b⁹.

Multiplying Like Bases with Coefficients

• STEP 1: Group terms with like bases.

• STEP 2: Multiply the coefficients of the like bases.

• STEP 3: Add the exponents of the like bases.

• (The base always stays the same.)

 (6y³)(3y⁵) 

STEP 1: (There are only two terms so they do not need grouped.)

STEP 2: (6 x 3) y^{(3 + 5)} = 18y⁸

Open Ended

Simplify (3mn²)(9m²n).

Power of a Power

To find the power of a power, multiply the exponents. 

Example

(k⁵)⁹ = k^{(5 x 9)} = k⁴⁵

Open Ended

(k³)⁴

Power of a Product

To find the power of a product, find the power of each factor and multiply.

Example

-(2y)² = (-1)(2²)(y²) = -4y²

Open Ended

(6x⁴)²