en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (sqrt(32))^{2/5}

Solution

simplify

(32)^{\frac{2}{5}}

Solution

2

Solution steps

(32)^{\frac{2}{5}}

32 = 42

= (42)^{\frac{2}{5}}

Apply exponent rule:

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

(42)^{\frac{2}{5}} = 4^{\frac{2}{5}} (2)^{\frac{2}{5}}

= 4^{\frac{2}{5}} (2)^{\frac{2}{5}}

(2)^{\frac{2}{5}} = 2^{\frac{1}{5}}

= 4^{\frac{2}{5}} \cdot 2^{\frac{1}{5}}

Factor integer

4 = 2^{2}

= (2^{2})^{\frac{2}{5}} \cdot 2^{\frac{1}{5}}

Apply exponent rule:

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

(2^{2})^{\frac{2}{5}} = 2^{2 \cdot \frac{2}{5}}

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

Refine

= 2^{\frac{4}{5}} \cdot 2^{\frac{1}{5}}

Apply exponent rule:

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

2^{\frac{4}{5}} \cdot 2^{\frac{1}{5}} = 2^{\frac{4}{5} + \frac{1}{5}}

= 2^{\frac{4}{5} + \frac{1}{5}}

Join

\frac{4}{5} + \frac{1}{5} : 1

= 2^{1}

Apply rule

a^{1} = a

= 2

Popular Examples

simplify sqrt(20)-sqrt(125)simplify

20 - 125

factor c^2-22c-968 factor

c^{2} - 22 c - 968

simplify sqrt(-2-2)simplify

- 2 - 2

simplify 1*10^{15}simplify

1 \cdot 1 0^{15}

simplify 1-(5/13)^2 simplify

1 - (\frac{5}{13})^{2}

Frequently Asked Questions (FAQ)

What is (sqrt(32))^{2/5} ?
The solution to (sqrt(32))^{2/5} is 2