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Calculate one-third to the fifth power times one-third to the second power all divided by one-third to the fourth power, giving your answer in its simplest form.
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Here we can see we’re multiplying and dividing.
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And all of our numbers have powers.
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They have exponents.
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It’s important to remember, when multiplying like basis, we can add their exponents.
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And when dividing, we can subtract their exponents.
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First, let’s work within the brackets.
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We have one-third to the fifth power times one-third to the second power.
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So that will be one-third to the five plus two power.
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And five plus two is seven.
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And now when dividing, so we can imagine these brackets aren’t here anymore, when dividing, we subtract our exponents.
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So we have one-third to the seven minus four power, which is equal to one-third cubed.
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So we need to cube the top and the bottom, the one and the three.
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One cubed is one and three cubed is 27, giving us a final answer: one 27th.
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Now we also could’ve solved this by strictly expanding and not using any of the properties.
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So we could’ve taken each fraction and raise it to the designated power, like we’ve done here.
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And we get one over 243 times one-ninth divided by one over 81.
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When multiplying fractions, we multiply straight across.
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We multiply the numerators together.
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And we multiply the denominators together.
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And we have one over 2187 divided by one over 81.
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Now when dividing, we actually multiplied by the second fraction’s reciprocal.
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So we have 81 over 2187 which reduces to one 27th.
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So once again, our answer, in its simplest form, will be one 27th.