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

1 Answer
Johnson Z.
Dec 31, 2015

#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#

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