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Popular >

simplify (-216x^{-9})^{1/3}

Solution

simplify

(- 216 x^{- 9})^{\frac{1}{3}}

Solution

- \frac{6}{x ^{3}}

Solution steps

(- 216 x^{- 9})^{\frac{1}{3}}

Apply exponent rule:

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

if

n

is odd

(- 216 x^{- 9})^{\frac{1}{3}} = - (216 x^{- 9})^{\frac{1}{3}}

= - (216 x^{- 9})^{\frac{1}{3}}

Apply exponent rule:

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

(216 x^{- 9})^{\frac{1}{3}} = 21 6^{\frac{1}{3}} (x^{- 9})^{\frac{1}{3}}

= - 21 6^{\frac{1}{3}} (x^{- 9})^{\frac{1}{3}}

21 6^{\frac{1}{3}} = 6

= - 6 (x^{- 9})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(x^{- 9})^{\frac{1}{3}} = x^{- 9 \cdot \frac{1}{3}}

= - 6 x^{- 9 \cdot \frac{1}{3}}

- 9 \cdot \frac{1}{3} = - 3

= - 6 x^{- 3}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

x^{- 3} = \frac{1}{x ^{3}}

= - 6 \cdot \frac{1}{x ^{3}}

Simplify

6 \cdot \frac{1}{x ^{3}} : \frac{6}{x ^{3}}

= - \frac{6}{x ^{3}}

Popular Examples

-1<= (9-2x)/5 <4

- 1 \leq \frac{9 - 2 x}{5} < 4

simplify (2pi)/(pi/3)simplify

\frac{2 π}{\frac{π}{3}}

\frac{u}{6} - 3 = 1

9+1/3 x>= 4-1/2 x

9 + \frac{1}{3} x \geq 4 - \frac{1}{2} x

1/2 (8a-20)=2(a+6)

\frac{1}{2} (8 a - 20) = 2 (a + 6)

Frequently Asked Questions (FAQ)

What is (-216x^{-9})^{1/3} ?
The solution to (-216x^{-9})^{1/3} is -6/(x^3)