What is (-32x^{-10}y^{15})^{1/5} ?

The solution to (-32x^{-10}y^{15})^{1/5} is -(2y^3)/(x^2)

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simplify (-32x^{-10}y^{15})^{1/5}

simplify

(- 32 x^{- 10} y^{15})^{\frac{1}{5}}

- \frac{2 y ^{3}}{x ^{2}}

Solution steps

(- 32 x^{- 10} y^{15})^{\frac{1}{5}}

Apply exponent rule:

(- a)^{\frac{1}{n}} = - (a)^{\frac{1}{n}},

n

is odd

(- 32 x^{- 10} y^{15})^{\frac{1}{5}} = - (32 x^{- 10} y^{15})^{\frac{1}{5}}

= - (32 x^{- 10} y^{15})^{\frac{1}{5}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(32 x^{- 10} y^{15})^{\frac{1}{5}} = 3 2^{\frac{1}{5}} (x^{- 10})^{\frac{1}{5}} (y^{15})^{\frac{1}{5}}

= - 3 2^{\frac{1}{5}} (x^{- 10})^{\frac{1}{5}} (y^{15})^{\frac{1}{5}}

3 2^{\frac{1}{5}} = 2

= - 2 (x^{- 10})^{\frac{1}{5}} (y^{15})^{\frac{1}{5}}

Simplify

(x^{- 10})^{\frac{1}{5}} : \frac{1}{x ^{2}}

= - 2 \cdot \frac{1}{x ^{2}} (y^{15})^{\frac{1}{5}}

Simplify

(y^{15})^{\frac{1}{5}} : y^{3}

= - 2 \cdot \frac{1}{x ^{2}} y^{3}

Simplify

2 \cdot \frac{1}{x ^{2}} y^{3} : \frac{2 y ^{3}}{x ^{2}}

= - \frac{2 y ^{3}}{x ^{2}}

6 x^{2} + 4 x - 3 = 0

\frac{2 x + 6}{x - 2} < 0

∣ 2 b + 6 ∣ = ∣ b + 1 ∣

45 b + 10

1 + 3 z \geq 7

What is (-32x^{-10}y^{15})^{1/5} ?
The solution to (-32x^{-10}y^{15})^{1/5} is -(2y^3)/(x^2)