Question

# Completely simplify the expression (2frac{x}{y^{-1/3}})^{-1} Your final answer should contain no negative exponents and no radicals.

Completely simplify the expression $$(2\frac{x}{y^{-1/3}})^{-1}$$ Your final answer should contain no negative exponents and no radicals.

2021-02-01
For negative in exponent, we can change the side of the term
$$(2\frac{x}{y^{-1/3}})^{-1}$$
$$=(2xy^{\frac{1}{3}})^{-1}$$
Then distribute -1 with other exponents
$$=2^{-1}x^{-1}(y^{\frac{1}{3}})^{1}$$
$$=\frac{1}{2} \cdot \frac{1}{x}y^{-\frac{1}{3}}$$
$$=\frac{1}{2xy^{\frac{1}{3}}}$$
Answer: $$=\frac{1}{2xy^{\frac{1}{3}}}$$