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Simplify π₯ to the π plus nine π¦ to the π plus four over π₯ to the π plus three times π¦ to the π.
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Here we notice that we have π₯ and π¦ in both the numerator and the denominator.
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Our first step to simplifying will be trying to get all of the π₯ and π¦s in the numerator.
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Remember that you can move a base to a certain exponent and the denominator to the numerator by taking its negative exponent.
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π₯ to the π plus nine was already there.
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And if we take π₯ to the negative π plus three, we can bring that value to the numerator.
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π¦ to the π plus four was already in the numerator.
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And we want to bring π¦ to the π into the numerator.
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So we take its negative exponent, π¦ to the negative π.
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What is the mathematical operation happening here?
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Itβs multiplication.
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All of these exponents are being multiplied together.
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And that means we need the exponent product rule.
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It tells us that π₯ to the π power times π₯ to the π power equals π₯ to the π plus π.
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When your bases are the same and youβre multiplying these two exponents together, you do that by adding the two exponents.
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We have two exponents with the base of π₯.
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We keep the base of π₯, and then we add their exponents together, π plus nine.
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Be careful with your negative there.
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You need to distribute that negative value across the π and the three.
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When we do that, we get π plus nine minus π minus three.
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Combine like terms.
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Plus π minus π cancels out.
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Nine minus three equals six.
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π₯ should be taken to the sixth power.
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We also have two exponents with a π¦ as a base.
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Weβll take π¦ to the π plus four plus negative π, π plus four minus π.
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Combining like terms, π minus π cancels out, leaving us with four.
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π¦ is being taken to the fourth power.
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Thereβs one more important thing.
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Remember that we were multiplying the π₯s and the π¦s together, and that means the final simplification is π₯ to the sixth times π¦ to the fourth.