Question

Write in simplest form using positive exponents in the answer:a^-6/a (a^-3)^2/a^-3

Answer 1

`a^(-x)=((1)/(a)^{})^x`

So:

`a^(-6)=((1)/(a))^6`

Now:

`(a^(-6))/(a)=((1)/(a))^6\cdot(1)/(a)=((1)/(a))^(6+1)=((1)/(a))^7=(1)/(a^7)`
`(a^(-3))^2=a^(-3\cdot2)=a^(-6)`

`\frac{\mleft(a^{\mleft\{-3\mright\}}\mright)^2}{a^(-3)}=(a^(-6))/(a^(-3))=(1)/(a^6)\cdot(1)/(a^(-3))=(1)/(a^(6-3))=(1)/(a^3)`

When you invert a fraction, you change the sign of the exponent.