Question

How do you evaluate `5^ { 3} \div 5^ { - 1}`?

Answer 1

`625`

Explanation:

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

`•color(white)(x)a^m/a^n=a^((m-n))`

`rArr5^3-:5^-1=5^3/5^-1`

`color(white)(xxxxxxxx)=5^(3-(-1))=5^4`

`color(white)(xxxxxxxxxx)=5xx5xx5xx5xx=625`

Answer 2

`5^4 = 625`

Explanation:

One of the laws of indices deals with negative indices:

`x^-m = 1/x^m" or "1/x^-n = x^n`

`5^3/color(blue)(5^-1) = 5^3 xx color(blue)(5^1)`

Another law of indices is `x^m xx x^n = x^(m+n)`

`5^3 xx 5^1 = 5^4`

`5^4 = 625`