Video: Simplifying Algebraic Expressions Using Laws of Exponents

Simplify 𝑥⁵ × 𝑥².

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Video Transcript

Simplify 𝑥 to the power of five multiplied by 𝑥 squared.

This expression can be simplified using one of the laws of indices: 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. In order to simplify 𝑥 to the power of five multiplied by 𝑥 squared, we need to add the exponents or indices. As five plus two is equal to seven, we can say that 𝑥 to the power of five multiplied by 𝑥 squared is equal to 𝑥 to the power of seven.

An alternative method would have been to have considered each term separately. 𝑥 to the five is equal to 𝑥 multiplied by 𝑥 multiplied by 𝑥 multiplied by 𝑥 multiplied by 𝑥 again and 𝑥 squared is the same as 𝑥 multiplied by 𝑥. How many 𝑥s do we have altogether? Well, we have seven of them. Therefore, we can write 𝑥 to the five multiplied by 𝑥 squared as 𝑥 to the power of seven.

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