Question

How do you use the laws of exponents to simplify the expression `((4^2)/(4^3))*(4)^-3`?

Answer 1

`1/256`

Explanation:

`"using the "color(blue)"laws of exponents"`

`•color(white)(x)a^m/a^nhArra^((m-n))`

`•color(white)(x)a^mxxa^nhArra^((m+n))`

`•color(white)(x)a^-mhArr1/a^m`

`rArr(4^2/4^3)xx4^-3`

`=4^((2-3))xx4^-3`

`=4^-1xx4^-3`

`=4^((-1+(-3)))=4^-4=1/4^4=1/256`

Answer 2

`1/4^4 or 4^-4`

Explanation:

When dividing like terms with powers you subtract the powers.

`4^2/4^3=4^(2-3)=4^(-1)`

When multiplying like terms with powers you add the powers

`(4^2/4^3)xx 4^-3=4^(-1)xx4^-3=4^(-1+ -3)4^(-1-3)=4^-4`