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Just need someone to clarify things with me!

As I was solving this equation, I got:

x^-2
-------
x^10

I moved x^-2 down with x^10

So in x^-2's place, I placed a positive 1.

1
----------------------
x^10 times x^-2

The radical rule here is to pretty much subtract ahead. However, this extremely smart person said something like if I move a negative number to the denominator, it becomes positive. However, in this case, x^-2 stays the same.

Anyone explain here??

Just Need Someone To Clarify Things With Me As I Was Solving This Equation I Got X2 X10 I Moved X2 Down With X10 So In X2s Place I Placed A Positive 1 1 X10 Tim class=

Sagot :

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Answer:

[tex]\frac{1}{x^{12} }[/tex]

Step-by-step explanation:

Given [tex](\frac{x}{x^{-5}})^{-2}[/tex]

The Negative Exponent Rule states that, [tex]a^{-n} = \frac{1}{a^{n}}[/tex]

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

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

[tex]\frac{1}{(\frac{x}{x^{-5}})^{2}} = \frac{1}{\frac{x^{2} }{(x^{-5})^{2}}}[/tex]  

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

[tex](x^{-5})^{2} = x^{-10}[/tex]

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

[tex]\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}}}}[/tex]    

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

So the denominator now becomes:

[tex]\frac{1}{\frac{x^{2} }{\frac{1}{x^{10}}}} = \frac{1}{x^{2}*x^{10} }[/tex]

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

   [tex]\frac{1}{x^{2}*x^{10} } = \frac{1}{x^{2+10}} = \frac{1}{x^{12} }[/tex]

Therefore, the correct answer is: [tex]\frac{1}{x^{12} }[/tex]

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