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Okay Shmoop math people Here we go Another drill for

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you What is the value of the quantity Negative to

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to the sixth power All right let's think about this

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one The most straightforward way to perform this kind of

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calculation would be to multiply negative too by itself Six

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times But well that's not terribly efficiently Not all the

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time Instead we can use the properties of exponents to

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take a shortcut Well the power rule for exponents tells

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us that when one term with exponents is raised to

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another exponents weaken simplify the expression by multiplying the two

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exponents In other words x to the a power that

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quantity to the b is the same as x to

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the quantity eight times be so we can use this

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route change the problem so that we can work with

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a familiar cube root and square root Familiar like we

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know two squared for without really been thinking about it

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Right So what does that give us Let's factor out

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something's here we got negative two to the six that

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quantity which is the same as negative too toothy three

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times two which is the same as a double quantity

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thing here negative two cubed and then square so if

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we do all that out that gets us negative eight

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squared right because two four eight would be to cuba

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And then we've got negative to cube being negative eight

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and negative Eight square to sixty four so negative to

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to the sixth power is positive sixty four and negative

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sixty four's and b might be tempting but it's incorrect

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because any imager raised two and even power must be

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a positive number So anyway that's it It's sixteen And

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yes you could have brute force this one just as

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easily But we're doing this says that the on the

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exam when they give you to the seventeenth power in

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the thirty fourth power you can kind of do it 00:01:42.163 --> [endTime] quicker and easier Hopefully good luck with that

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