Question

Just need someone to clarify things with me!

Answer 1

Answer:

$\frac{1}{x^{12} }$

Step-by-step explanation:

Given $(\frac{x}{x^{-5}})^{-2}$

The Negative Exponent Rule states that, $a^{-n} = \frac{1}{a^{n}}$

Basically, since you're raising the fraction inside the parenthesis to a negative exponent, the whole fraction becomes a denominator of 1:  $\frac{1}{(\frac{x}{x^{-5}})^{2}}$

Then, you'll have to work on the denominator:

$\frac{1}{(\frac{x}{x^{-5}})^{2}} = \frac{1}{\frac{x^{2} }{(x^{-5})^{2}}}$  

Next, you'll have to work on the divisor of x² (in the denominator), $(x^{-5})^{2}$ by using the Power-to-Power Rule of Exponents: $(a^{m})^{n} = a^{mn}$, which results in:

$(x^{-5})^{2} = x^{-10}$

Since it is a negative exponent, you'll have to apply the Negative Exponent Rule once again to the denominator.

$\frac{1}{(\frac{x}{x^{-5}})^{2}} = \frac{1}{\frac{x^{2} }{(x^{-5})^{2}}} = \frac{1}{\frac{x^{2} }{x^{-10}}} = \frac{1}{\frac{x^{2} }{\frac{1}{x^{10}}}}$    

At this point, you could apply the Fraction rule onto the denominator: $\frac{a}{\frac{b}{c}} = \frac{a*c}{b}$

So the denominator now becomes:

$\frac{1}{\frac{x^{2} }{\frac{1}{x^{10}}}} = \frac{1}{x^{2}*x^{10} }$

Finally, you could apply the Product Rule of Exponents, $a^{m}a^{n} = a^{m + n }$ onto the denominator:

   $\frac{1}{x^{2}*x^{10} } = \frac{1}{x^{2+10}} = \frac{1}{x^{12} }$

Therefore, the correct answer is: $\frac{1}{x^{12} }$

Answer 2

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