Question

Simplify the following expression to simplest form using only positive exponents. 5

Answer 1

$\frac{16y^{28}}{x^{16}}$

Explanation:

Exponent rule :

$(a*b)^n\text{ = a}^2b^n$

$(32x^{-20}y^{35})^{-\frac{4}{5}}=\text{ 32}^{\frac{4}{5}}(x^{-20})^{\frac{4}{5}}(y^{35})^{\frac{4}{5}}$

Since

$32^{\frac{4}{5}}\text{ = 16}$

You can replace it in the equation

$16(x^{-20})^{\frac{4}{5}}(y^{35})^{\frac{4}{5}}$

Since

$Simplified\text{ : }(x^{-20})^{\frac{4}{5}}\text{ = }\frac{1}{x^{16}}$$Simplified\text{ : \lparen}y^{35})^{\frac{4}{5}}\text{ = }y^{28}$

You can replace them in the equation

$16*\frac{1}{x^{16}}*y^{28}\text{ = }\frac{16y^{28}}{x^{16}}$