Exponent Problem please help

[maxte]

Hi

I have this problem 2^-1 w^-2 x^3/ (4w^-1 x^3)^-2

Mathway shows the answer as 8x^9/(w^4) which leads to my confusion as to what exactly happens to the 2^-1.

I got as far as having the denominator be 2w^4 due to flipping the 2 down to change the exponent from negative to positive but i cant find why Mathway's answer makes the 2 disappear.

Please help me understand why.

Thanks!

 

[srmichael]

Hi

I have this problem 2^-1 w^-2 x^3/ (4w^-1 x^3)^-2

Mathway shows the answer as 8x^9/(w^4) which leads to my confusion as to what exactly happens to the 2^-1.

I got as far as having the denominator be 2w^4 due to flipping the 2 down to change the exponent from negative to positive but i cant find why Mathway's answer makes the 2 disappear.

Please help me understand why.

Thanks!

These can be tricky if you try and combine too many steps at once.

$\displaystyle \dfrac{2^{-1}w^{-2}x^3}{(4w^{-1}x^3)^{-2}}$

$\displaystyle \dfrac{2^{-1}w^{-2}x^3}{4^{-2}w^2x^{-6}}$

$\displaystyle \dfrac{4^2x^3x^6}{2w^2w^2}$

Can you take it from here?

Within my steps I am utilizing these rules:

$\displaystyle (a^m)^n=a^{mn}$

$\displaystyle a^{-m}=\dfrac{1}{a^m}$

 

[maxte]

These can be tricky if you try and combine too many steps at once.

$\displaystyle \dfrac{2^{-1}w^{-2}x^3}{(4w^{-1}x^3)^{-2}}$

$\displaystyle \dfrac{2^{-1}w^{-2}x^3}{4^{-2}w^2x^{-6}}$

$\displaystyle \dfrac{4^2x^3x^6}{2w^2w^2}$

Can you take it from here?

Within my steps I am utilizing these rules:

$\displaystyle (a^m)^n=a^{mn}$

$\displaystyle a^{-m}=\dfrac{1}{a^m}$

I just realized my mistake in multiplying 4 by -2 instead of using it as ^-2

Thank you!