How do you simplify a^-1/b^-1 and write it using only positive exponents?

Mar 1, 2017

Since ${a}^{- 1} = \frac{1}{a} \mathmr{and} {b}^{- 1} = \frac{1}{b}$

Explanation:

$= \frac{1}{a} \div \frac{1}{b}$

Dividing by a fraction = multiplying with the inverse:

$= \frac{1}{a} \times \frac{b}{1} = \frac{b}{a}$

Mar 1, 2017

$\frac{b}{a}$
When dealing with negative exponents the way I handle them is by knowing that a negative exponent is really just saying $\frac{1}{a} ^ x$ so in this case ${a}^{-} \frac{1}{b} ^ - 1$ really just means $\frac{\frac{1}{a} ^ 1}{\frac{1}{b} ^ 1}$ and so rewriting this we'll get $\frac{1}{a} \cdot \frac{b}{1}$ (I didn't include the exponents because ${a}^{1}$ is just a).
Multiply and you'll get $\frac{b}{a}$