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1/ (gg^2 e^5)^2 Write your answer with only positive exponents

1 Gg2 E52 Write Your Answer With Only Positive Exponents class=

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ANSWER

[tex]\frac{1}{g^6e^{10}}[/tex]

EXPLANATION

In the denominator, we have the product of g and g². The product of two powers with the same base is the base raised to the sum of the exponents,

[tex]\frac{1}{(gg^2e^5)^2}=\frac{1}{(g^{2+1}e^5)^2}=\frac{1}{(g^3e^5)^2}[/tex]

Now, we also have the power of a product. The exponents can be distributed into the multiplication,

[tex]\frac{1}{(g^3e^5)^2}=\frac{1}{(g^3)^2(e^5)^2}[/tex]

And finally, for both g and e, we have the power of a power. The result is the base raised to the product of the exponents,

[tex]\frac{1}{(g^3)^2(e^5)^2}=\frac{1}{g^{3\cdot2}e^{5\cdot2}^{}}=\frac{1}{g^6e^{10}}[/tex]

Hence, the simplified expression is,

[tex]\frac{1}{g^6e^{10}}[/tex]

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