en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt(4)^5

Solution

simplify

4^{5}

Solution

32

Solution steps

(4)^{5}

Apply exponent rule:

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

(4)^{4 + 1} = (4)^{4} 4

= (4)^{4} 4

(4)^{4} = ((4)^{2})^{2}

= ((4)^{2})^{2} 4

Apply exponent rule:

(4)^{2} = 4

= 4^{2} 4

Apply radical rule:

a = a^{\frac{1}{2}}

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

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

Apply exponent rule:

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

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

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

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

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

Factor the number:

4 = 2^{2}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

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

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

= 2^{5}

2^{5} = 32

= 32

Popular Examples

simplify (2.65*10^{-3})(10)simplify

(2.65 \cdot 1 0^{- 3}) (10)

simplify (ab)(ab^2)simplify

(ab) (a b^{2})

simplify \sqrt[3]{(27)^2}simplify

simplify e^{-0.29}simplify

e^{- 0.29}

simplify (9\sqrt[3]{9})(5\sqrt[3]{3})simplify

Frequently Asked Questions (FAQ)

What is sqrt(4)^5 ?
The solution to sqrt(4)^5 is 32