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Popular >

simplify 1/(8^{1/2)}

Solution

simplify

\frac{1}{8 ^{\frac{1}{2}}}

Solution

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

+1

Solution steps

\frac{1}{8 ^{\frac{1}{2}}}

Prime factorization of

8 : 2^{3}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

What is 1/(8^{1/2)} ?
The solution to 1/(8^{1/2)} is 1/(2*2^{1/2)}