Video: Simplifying Algebraic Expressions Using Laws of Exponents

Simplify (𝑥³)².

01:25

Video Transcript

Simplify 𝑥 cubed all squared.

The first thing to consider here is what we mean by squared. Squaring a number or expression means multiplying it by itself. Therefore, 𝑥 cubed squared means 𝑥 cubed multiplied by 𝑥 cubed. In order to simplify this, we need to consider 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.

When we are multiplying, we can add the exponents or indices. Adding three and three gives us an answer of six. Therefore, 𝑥 cubed all squared is equal to 𝑥 to the power of six. This leads us to a quicker method to solve the initial problem.

One of the other laws of indices states that 𝑥 to the power of 𝑎 to the power of 𝑏 is equal to 𝑥 to the power of 𝑎 multiplied by 𝑏. In our example, this means that we can rewrite 𝑥 cubed all squared as 𝑥 to the power of three times two. Three multiplied by two is equal to six. Therefore, our answer is 𝑥 to the power of six.

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