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Kathryn Kingham

Write an equivalent expression to (𝑥⁷𝑦⁵/𝑧⁵)³ that does not include parentheses.

Write an equivalent expression to 𝑥 to the seventh, 𝑦 to the fifth, over 𝑧 to the fifth all to the third power that does not include parenthesis. What does that mean?

It means that if we want to get rid of these parenthesis, we’ll need to distribute our to the third power to each of our terms, like this.

It means we’ll have to take 𝑥 to the seventh to the third power, 𝑦 to the fifth power to the third power, and 𝑧 to the fifth to the third power.

Now I’ve done this distribution, but I’ve included parenthesis here. So we need to get rid of these parenthesis as well. This is when we would use our power to a power rule, which says that to raise a power to a power you need to multiply the exponents together. To raise 𝑥 to the seventh power to the third power, I’ll need to multiply seven times three. And for the 𝑦 term, I’ll need to multiply five times three. The 𝑧 term will also be five times three, which will give me 𝑥 to the 21st power 𝑦 to the 15th power over 𝑧 to the 15th power. This is how we would write that expression without parentheses.

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