When you have a negative exponent, you move the variable with the negative exponent to the other side of the fraction to make the exponent positive.
For example:
[tex]x^{-3}[/tex] or [tex]\frac{x^{-3}}{1} =\frac{1}{x^3}[/tex]
[tex]\frac{1}{y^{-2}} =\frac{y^2}{1}[/tex] or [tex]y^2[/tex]
When you multiply an exponent directly to a variable with an exponent, you multiply the exponents together.
For example:
[tex](x^3)^2=x^{(3*2)}=x^6[/tex]
[tex](x^{\frac{1}{2}} )^{\frac{3}{2} }=x^{(\frac{1}{2} *\frac{3}{2} )}=x^{\frac{3}{4} }[/tex]
When you multiply an exponent directly to a fraction, you multiply the exponent to the top and bottom of the fraction.
For example:
[tex](\frac{x}{y} )^2[/tex] or [tex](\frac{x^1}{y^1} )^2=\frac{x^{(1*2)}}{y^{(1*2)}} =\frac{x^2}{y^2}[/tex]
[tex](y^2*z^{-\frac{1}{4}})^{\frac{5}{2} }[/tex] First make all of the exponents positive
[tex](\frac{y^2}{z^{\frac{1}{4}} } )^{\frac{5}{2} }[/tex] Now multiply the exponent into the fraction
[tex]\frac{y^{(2*\frac{5}{2})} }{z^{(\frac{1}{4}*\frac{5}{2} )} } =\frac{y^5}{z^{\frac{5}{8} } }[/tex] [y^(5) ÷ z^(5/8)]
