Question

How do you write the product of the expression `5^4*5^-7` using a positive exponent?

Answer 1

`1/5^3`

Explanation:

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

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^mxxa^n=a^(m+n)" and " a^-mhArr1/a^m)color(white)(2/2)|)))`

`rArr5^4xx5^-7=5^-3=1/5^3`

Answer 2

`1/5^3`

Explanation:

Another approach is to get rid of the negative index first..

Recall: `x^-m = 1/x^(+m)" and "x^m/x^n = 1/x^(n-m) if n>m`

`5^4 xx 5^-7`

=`5^4 xx 1/5^7`

=`1/5^(7-4)`

=`1/5^3`