en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify \sqrt[4]{-64}^3

Solution

simplify

Solution

16 (- 1)^{\frac{3}{4}} 2

Solution steps

Apply radical rule:

= ((- 64)^{\frac{1}{4}})^{3}

Apply exponent rule:

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

= (- 64)^{\frac{1}{4} \cdot 3}

\frac{1}{4} \cdot 3 = \frac{3}{4}

= (- 64)^{\frac{3}{4}}

Apply exponent rule:

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

(- 64)^{\frac{3}{4}} = (- 1)^{\frac{3}{4}} \cdot 6 4^{\frac{3}{4}}

= (- 1)^{\frac{3}{4}} \cdot 6 4^{\frac{3}{4}}

Apply exponent rule:

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

= (- 1)^{\frac{3}{4}} \cdot 2^{3} \cdot 4^{\frac{3}{4}}

4^{\frac{3}{4}} = 2^{\frac{3}{2}}

= 2^{3} (- 1)^{\frac{3}{4}} \cdot 2^{\frac{3}{2}}

2^{\frac{3}{2}} = 22

= 2^{3} \cdot 2 (- 1)^{\frac{3}{4}} 2

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{3} \cdot 2 = 2^{3 + 1}

= (- 1)^{\frac{3}{4}} \cdot 2^{3 + 1} 2

Add the numbers:

3 + 1 = 4

= (- 1)^{\frac{3}{4}} \cdot 2^{4} 2

2^{4} = 16

= 16 (- 1)^{\frac{3}{4}} 2

Popular Examples

simplify te^{-12t}simplify

t e^{- 12 t}

simplify 66e^{(-147x)}simplify

66 e^{(- 147 x)}

simplify 4e^{4x}*9e^{-3x}simplify

4 e^{4 x} \cdot 9 e^{- 3 x}

simplify (e^{x^2+2x-4})/(e^{5x+4)}simplify

\frac{e ^{x^{2} + 2 x - 4}}{e ^{5 x + 4}}

simplify e^{-j*(2pi)/8*0}simplify

e^{- j \cdot \frac{2 π}{8} \cdot 0}

Frequently Asked Questions (FAQ)

What is \sqrt[4]{-64}^3 ?
The solution to \sqrt[4]{-64}^3 is 16(-1)^{3/4}sqrt(2)