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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.
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What does that mean?
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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.
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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.
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Now I’ve done this distribution, but I’ve included parenthesis here.
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So we need to get rid of these parenthesis as well.
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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.
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To raise 𝑥 to the seventh power to the third power, I’ll need to multiply seven times three.
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And for the 𝑦 term, I’ll need to multiply five times three.
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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.
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This is how we would write that expression without parentheses.