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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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