# Math Help - explanation of algebra question

1. ## explanation of algebra question

hi there, trying to understand this expression.

$5^{4-x}$

is the same as:
$

= (\frac{1}{5})^{x-4}
$

im not really understanding what it does to get that. any1 ? thank u

2. Originally Posted by jvignacio
hi there, trying to understand this expression.

$5^{4-x}$

is the same as:
$

= (\frac{1}{5})^{x-4}
$

im not really understanding what it does to get that. any1 ? thank u

One of the laws of exponents says:

$a^{m}=\left(\frac{1}{a}\right)^{-m} \ \ or \ \ \left(\frac{a}{b}\right)^{-m}=\left(\frac{b}{a}\right)^m$

$5^{4-x}=\left(\frac{1}{5}\right)^{-(4-x)}=\left(\frac{1}{5}\right)^{(-4+x)}=\left(\frac{1}{5}\right)^{(x-4)}$

3. Originally Posted by masters
One of the laws of exponents says:

$a^{m}=\left(\frac{1}{a}\right)^{-m} \ \ or \ \ \left(\frac{a}{b}\right)^{-m}=\left(\frac{b}{a}\right)^m$

$5^{4-x}=\left(\frac{1}{5}\right)^{-(4-x)}=\left(\frac{1}{5}\right)^{(-4+x)}=\left(\frac{1}{5}\right)^{(x+4)}$

oh mate just wat i needed. cheers.

4. Originally Posted by jvignacio
oh mate just wat i needed. cheers.
I changed a sign in my original answer in the last step. Exponent should be x-4, not x+4. Sorry. Typing too fast. My original post is correct now.