myarauch myarauch
  • 22-10-2019
  • Mathematics
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What is the value of the power a if 5 to the power of a is equal to 1/125

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Аноним Аноним
  • 22-10-2019

First of all, you should know/notice that

[tex]125=5^3[/tex]

You should also know how negative exponents work:

[tex]a^{-m}=\dfrac{1}{a^m}[/tex]

So, if you wanted

[tex]5^x=125[/tex]

the answer would be x=3, but since you want 125 to be at the denominator, the answer is x=-3:

[tex]5^{-3}=\dfrac{1}{5^3}=\dfrac{1}{125}[/tex]

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