Question

How do you simplify `sqrt(x^14 y^21) / z^-35`?

Answer 1

`x^7y^(21/2)z^35`

Explanation:

According to the exponent rule, `a^-b=1/a^b` , start by rewriting `z^-35` so that it has a positive exponent.

`sqrt(x^14y^21)/z^-35`

`=sqrt(x^14y^21)/(1/z^35)`

Divide the numerator by the denominator.

`=sqrt(x^14y^21)-:1/z^35`

Simplify.

`=sqrt(x^14y^21)*z^35/1`

`=sqrt(x^14y^21)z^35`

As a shortcut, since you know that `z^-35` has a negative exponent, to make the term have a positive exponent, you could have also just moved it to the numerator and changed the negative exponent to a positive exponent. For example:

`sqrt(x^14y^21)/z^-35rArrsqrt(x^14y^21)z^35`

Going on, recall that `sqrt(color(white)(x)` is multiplying an exponent by `color(red)(1/2)` (or dividing by `2`).

`=sqrt(x^14y^21)z^35`

`=sqrt(x^14)sqrt(y^21)z^35`

`=x^(14*color(red)(1/2))y^(21*color(red)(1/2))z^35`

Simplify.

`=x^7y^(21/2)z^35`