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Popular >

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

Solution

simplify

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

Solution

\frac{1}{4 x}

Solution steps

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

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

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

= \frac{1}{4} x^{- 1}

Apply exponent rule:

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

x^{- 1} = \frac{1}{x}

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

Simplify

\frac{1}{4} \cdot \frac{1}{x} : \frac{1}{4 x}

= \frac{1}{4 x}

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\frac{1}{2 π \cdot 0.8761 \cdot 1 0 ^{3} \cdot 2.2 \cdot 1 0 ^{- 6}}

Frequently Asked Questions (FAQ)

What is (1/2 x^{-1/2})^2 ?
The solution to (1/2 x^{-1/2})^2 is 1/(4x)