Video: Simplifying Algebraic Expressions Using Laws of Exponents

Simplify 𝑏⁴ × 𝑎⁴ × 𝑏² × 𝑎⁵.

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Video Transcript

Simplify 𝑏 to the power of four multiplied by 𝑎 to the power of four multiplied by 𝑏 to the power of two multiplied by 𝑎 to the power of five.

Our first step is to group the like terms: 𝑎 to the power of four multiplied by 𝑎 to the power of five and the 𝑏 terms, 𝑏 to the power of four multiplied by 𝑏 to the power of two. We can then use one of the laws of exponents. 𝑥 to the power of 𝑎 multiplied by 𝑥 to the power of 𝑏 is equal to 𝑥 to the power of 𝑎 plus 𝑏.

Using this law on the 𝑎 terms, 𝑎 to the power of four multiplied by 𝑎 to the power of five means that we can add the two exponents or powers, giving us 𝑎 to the power of four plus five. In the same way, we can add the exponents or powers of the 𝑏 terms, 𝑏 to the power of four plus two. Four plus five is equal to nine, and four plus two is equal to six.

Therefore, simplifying this expression gives us 𝑎 to the power of nine multiplied by 𝑏 to the power of six. As multiplication is commutative, this could also be written as 𝑏 to the power of six multiplied by 𝑎 to the power of nine.

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