Question

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

Answer 1

$a^{-x}=(\frac{1}{a}^{})^x$

So:

$a^{-6}=(\frac{1}{a})^6$

Now:

$\frac{a^{-6}}{a}=(\frac{1}{a})^6\cdot\frac{1}{a}=(\frac{1}{a})^{6+1}=(\frac{1}{a})^7=\frac{1}{a^7}$$(a^{-3})^2=a^{-3\cdot2}=a^{-6}$

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

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