What is 3*0.24^{-1/2} ?

The solution to 3*0.24^{-1/2} is (3^{1/2}*5)/(2^{1/2)}

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simplify 3*0.24^{-1/2}

simplify

3 \cdot 0.2 4^{- \frac{1}{2}}

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

Decimal Notation

6.12372 \dots

Solution steps

3 \cdot 0.2 4^{- \frac{1}{2}}

Apply exponent rule:

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

0.2 4^{- \frac{1}{2}} = \frac{1}{0.2 4 ^{\frac{1}{2}}}

= 3 \cdot \frac{1}{0.2 4 ^{\frac{1}{2}}}

0.2 4^{\frac{1}{2}} = \frac{6 ^{\frac{1}{2}}}{5}

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

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

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

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

8 \cdot (x^{4} y^{4})

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