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#### PistolSlap

##### New member

- Jan 13, 2013

- 2

I have this problem to simplify with positive exponents:

\[\left[(-4a^{-4}b^{-5})^{-3}\right]^4\]

So, working with the interior brackets, I applied -3 to the equation, which resulted in:

\[-(-64)x^{12}b^{15}\]

**because "-4" was not in brackets, the exponent was applied to the 4 only, independent of the negative sign, which resulted in -(-64), so:

\[\left[ 64x^{12}b^{15}\right]^4\]

which resulted in this insane answer:

\[16777216x^{48}b^{60}\]

However, when I checked it, an online calculator said the answer was:

\[\frac{a^{48}b^{60}}{16777216}\]

which means that when applying exponents to the number I did something wrong, as it should have ended up negative, which would have resulted in it becoming a positive denominator.

What did I do wrong to end up with the wrong sign on that number?

\[\left[(-4a^{-4}b^{-5})^{-3}\right]^4\]

So, working with the interior brackets, I applied -3 to the equation, which resulted in:

\[-(-64)x^{12}b^{15}\]

**because "-4" was not in brackets, the exponent was applied to the 4 only, independent of the negative sign, which resulted in -(-64), so:

\[\left[ 64x^{12}b^{15}\right]^4\]

which resulted in this insane answer:

\[16777216x^{48}b^{60}\]

However, when I checked it, an online calculator said the answer was:

\[\frac{a^{48}b^{60}}{16777216}\]

which means that when applying exponents to the number I did something wrong, as it should have ended up negative, which would have resulted in it becoming a positive denominator.

What did I do wrong to end up with the wrong sign on that number?

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