en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 16^{5/6}*4^{5/6}

Solution

simplify

1 6^{\frac{5}{6}} \cdot 4^{\frac{5}{6}}

Solution

32

Solution steps

1 6^{\frac{5}{6}} \cdot 4^{\frac{5}{6}}

4^{\frac{5}{6}} = 2 \cdot 2^{\frac{2}{3}}

= 1 6^{\frac{5}{6}} \cdot 2 \cdot 2^{\frac{2}{3}}

2 \cdot 2^{\frac{2}{3}} = 2^{\frac{5}{3}}

= 1 6^{\frac{5}{6}} \cdot 2^{\frac{5}{3}}

Factor integer

16 = 2^{4}

= (2^{4})^{\frac{5}{6}} \cdot 2^{\frac{5}{3}}

Apply exponent rule:

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

(2^{4})^{\frac{5}{6}} = 2^{4 \cdot \frac{5}{6}}

= 2^{4 \cdot \frac{5}{6}} \cdot 2^{\frac{5}{3}}

Refine

= 2^{\frac{10}{3}} \cdot 2^{\frac{5}{3}}

Apply exponent rule:

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

2^{\frac{10}{3}} \cdot 2^{\frac{5}{3}} = 2^{\frac{10}{3} + \frac{5}{3}}

= 2^{\frac{10}{3} + \frac{5}{3}}

Join

\frac{10}{3} + \frac{5}{3} : 5

= 2^{5}

2^{5} = 32

= 32

Popular Examples

simplify (1/e-1/(e^2))*(1/e-1/(e^2))simplify

(\frac{1}{e} - \frac{1}{e ^{2}}) \cdot (\frac{1}{e} - \frac{1}{e ^{2}})

simplify (x-2)(e^{-x})simplify

(x - 2) (e^{- x})

simplify 12/300*e^{-(30)/(300(16))}simplify

\frac{12}{300} \cdot e^{- \frac{30}{300 ( 16 )}}

simplify 2pi(10)100*10^{-6}simplify

2 π (10) 100 \cdot 1 0^{- 6}

simplify \sqrt[7]{x^{7a+b}}simplify

Frequently Asked Questions (FAQ)

What is 16^{5/6}*4^{5/6} ?
The solution to 16^{5/6}*4^{5/6} is 32