Simplify: Write Answer Only Using Positive Exponents

**SSK** · February 1st 2010, 09:08 PM

(2x^-2 y^3/6xz^5)^-4

Answer is 81x^12 z^20/y^12

how is this so?

**Grandad** · February 2nd 2010, 03:04 AM

Hello SSK

Originally Posted by SSK

(2x^-2 y^3/6xz^5)^-4

Answer is 81x^12 z^20/y^12

how is this so?

First, invert the fraction to get rid of the negative power outside the bracket:

$\left(\frac{2x^{-2} y^3}{6xz^5}\right)^{-4}=\left(\frac{6xz^5}{2x^{-2} y^3}\right)^{4}$

Then move the $x^{-2}$ term to the numerator to get rid of its negative power:

$=\left(\frac{6xz^5x^2}{2 y^3}\right)^{4}$

(By the way, what I should more correctly say is: multiply top-and-bottom by $x^2$ , and then note that in the denominator $x^{-2}\times x^2 = 1$ . But it's quicker to say: move the $x^{-2}$ term ...)

Simplify:

$=\left(\frac{3x^3z^5}{y^3}\right)^{4}$

Lastly, remove the brackets by raising everything to the power $4$ :

$=\frac{81x^{12}z^{20}}{y^{12}}$

Grandad

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