en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 125^{-1/2}

Solution

simplify

12 5^{- \frac{1}{2}}

Solution

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

+1

Decimal Notation

0.0894427191

Solution steps

12 5^{- \frac{1}{2}}

Prime factorization of

125 : 5^{3}

= (5^{3})^{- \frac{1}{2}}

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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

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

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

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

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

Popular Examples

x^{2} + 4 x \geq 0

3 (5 x + 1) = 48

7 x^{2} + 2 x + 8 = 0

7x-6(3x-5)<5x-3(4x+8)

7 x - 6 (3 x - 5) < 5 x - 3 (4 x + 8)

factor x^3-11x^2+23x+35 factor

x^{3} - 11 x^{2} + 23 x + 35

Frequently Asked Questions (FAQ)

What is 125^{-1/2} ?
The solution to 125^{-1/2} is 1/(5*5^{1/2)}