en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (-27x^{-15})^{1/3}

Solution

simplify

(- 27 x^{- 15})^{\frac{1}{3}}

Solution

- \frac{3}{x ^{5}}

Solution steps

(- 27 x^{- 15})^{\frac{1}{3}}

Apply exponent rule:

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

if

n

is odd

(- 27 x^{- 15})^{\frac{1}{3}} = - (27 x^{- 15})^{\frac{1}{3}}

= - (27 x^{- 15})^{\frac{1}{3}}

Apply exponent rule:

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

(27 x^{- 15})^{\frac{1}{3}} = 2 7^{\frac{1}{3}} (x^{- 15})^{\frac{1}{3}}

= - 2 7^{\frac{1}{3}} (x^{- 15})^{\frac{1}{3}}

2 7^{\frac{1}{3}} = 3

= - 3 (x^{- 15})^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0

(x^{- 15})^{\frac{1}{3}} = x^{- 15 \cdot \frac{1}{3}}

= - 3 x^{- 15 \cdot \frac{1}{3}}

- 15 \cdot \frac{1}{3} = - 5

= - 3 x^{- 5}

Apply exponent rule:

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

x^{- 5} = \frac{1}{x ^{5}}

= - 3 \cdot \frac{1}{x ^{5}}

Simplify

3 \cdot \frac{1}{x ^{5}} : \frac{3}{x ^{5}}

= - \frac{3}{x ^{5}}

Popular Examples

factor 28e^5-35e^2 factor

28 e^{5} - 35 e^{2}

factor-4y^4+6y^2-14y factor

- 4 y^{4} + 6 y^{2} - 14 y

2(4x+1)(x-1)+3=0

2 (4 x + 1) (x - 1) + 3 = 0

\frac{x ^{2}}{3} = 12

(x-5)/(4x-4)+2/(x^2-1)>= 0

\frac{x - 5}{4 x - 4} + \frac{2}{x ^{2} - 1} \geq 0

Frequently Asked Questions (FAQ)

What is (-27x^{-15})^{1/3} ?
The solution to (-27x^{-15})^{1/3} is -3/(x^5)