Products of Powers Example

​The Products of Powers property states that to multiply powers with the SAME BASE, you must add their exponents.

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a^m (aⁿ) = a^m+n​

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​9xy²⋅9x⁵y²

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Step 1:

Reorder (use the Commutative Property)​

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9 ⋅​ 9 ⋅ x¹ ⋅ x⁵ ⋅ y² ⋅ y²

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​

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​9xy²⋅9x⁵y²

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Step 2:​

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​Use the Associative Property to group like terms & multiply the coefficients.

9 ⋅​ 9 = 81

81 ⋅​ x¹ ⋅ x⁵ ⋅ y² ⋅ y²

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​9xy²⋅9x⁵y²

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Step 3:​

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​Use the Product of Powers Property to add the exponents.

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81 ⋅​ x¹ ⋅ x⁵ ⋅ y² ⋅ y²

81 ⋅​ (x¹⁺⁵) ⋅ (y²⁺²)

81 ⋅​ x⁶ ⋅ y⁴

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​9xy²⋅9x⁵y²

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Step 4:​

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​Simplify

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81x⁶y⁴

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Multiple Choice

Simplify 3u⁴v⁵ ⋅ 7u²v³

• 21u²v⁸

• -21u⁶v⁸

• 21u⁶v⁸