How do you simplify (2x^-6)/(7y^-3)^-3 using only positive exponents?

Apr 27, 2017

$\frac{686}{{x}^{6} {y}^{9}}$

Explanation:

Given: $\frac{2 {x}^{-} 6}{7 {y}^{-} 3} ^ - 3$

Use the exponent rules ${x}^{-} n = \frac{1}{x} ^ n \text{ and } \frac{1}{x} ^ - m = {x}^{m}$

And the exponent power rule ${\left({x}^{m} {y}^{n}\right)}^{c} = {x}^{m \cdot c} {y}^{n \cdot c}$

$\frac{2 {x}^{-} 6}{7 {y}^{-} 3} ^ - 3 = \frac{2}{{x}^{6} \left({7}^{-} 3 {y}^{9}\right)} = \frac{2 \cdot {7}^{3}}{{x}^{6} {y}^{9}} = \frac{2 \cdot 343}{{x}^{6} {y}^{9}} = \frac{686}{{x}^{6} {y}^{9}}$