Question

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

Answer 1

`(1)/(g^6e^(10))`

Step-by-step 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,

`(1)/((gg^2e^5)^2)=(1)/((g^(2+1)e^5)^2)=(1)/((g^3e^5)^2)`

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

`(1)/((g^3e^5)^2)=(1)/((g^3)^2(e^5)^2)`

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,

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

Hence, the simplified expression is,

`(1)/(g^6e^(10))`