en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/4 (16)^{-3/4}

Solution

simplify

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

Solution

\frac{1}{32}

+1

Decimal Notation

0.03125

Solution steps

\frac{1}{4} \cdot 1 6^{- \frac{3}{4}}

Factor the number:

16 = 2^{4}

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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

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

= \frac{1}{4} \cdot \frac{1}{2 ^{3}}

2^{3} = 8

= \frac{1}{4} \cdot \frac{1}{8}

\frac{1}{4} \cdot \frac{1}{8} = \frac{1}{32}

= \frac{1}{32}

Popular Examples

simplify 3/2 (-2)^{3-1}simplify

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

∣ 2 x - 1 ∣ \leq 1

x^{4} - 9 x^{2} + 8 = 0

9 x + 5 - 8 x + 14 = 20

simplify (18x^3y^3)/(12x^4y^7)simplify

\frac{18 x ^{3} y ^{3}}{12 x ^{4} y ^{7}}

Frequently Asked Questions (FAQ)

What is 1/4 (16)^{-3/4} ?
The solution to 1/4 (16)^{-3/4} is 1/32