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Evaluate 27 to the power of negative one-third.
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In this question, we can see that we have a negative exponent of negative a third.
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So letβs start by changing this negative exponent into a positive one.
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To do this, weβre going to use the exponent rule that if we have a negative exponent, for example, π to the power of negative π, then we can write this with a positive exponent as one over π to the power of π.
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So taking our 27 to the power of negative one-third, we can write this as one over 27 to the power of one-third.
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Considering our value 27 to the power of one-third, what does that actually mean?
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Well, itβs the same as the cube root of 27.
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So for the cube root of 27, weβre trying to find a value π₯ that will give us π₯ times π₯ times π₯ equals 27.
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Since we know that three times three times three will give us 27, then the cube root of 27 is three.
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So our complete value will be one over three.
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And therefore 27 to the power of negative one-third is equal to one-third.