What is (148)^{3/2} ?

The solution to (148)^{3/2} is 296*37^{1/2}

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simplify (148)^{3/2}

simplify

(148)^{\frac{3}{2}}

296 \cdot 3 7^{\frac{1}{2}}

Decimal Notation

1800.49770 \dots

Solution steps

14 8^{\frac{3}{2}}

Prime factorization of

148 : 2^{2} \cdot 37

= (2^{2} \cdot 37)^{\frac{3}{2}}

Apply exponent rule:

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

(2^{2} \cdot 37)^{\frac{3}{2}} = (2^{2})^{\frac{3}{2}} \cdot 3 7^{\frac{3}{2}}

= (2^{2})^{\frac{3}{2}} \cdot 3 7^{\frac{3}{2}}

(2^{2})^{\frac{3}{2}} = 8

= 8 \cdot 3 7^{\frac{3}{2}}

3 7^{\frac{3}{2}} = 37 \cdot 3 7^{\frac{1}{2}}

= 8 \cdot 37 \cdot 3 7^{\frac{1}{2}}

Multiply the numbers:

8 \cdot 37 = 296

= 296 \cdot 3 7^{\frac{1}{2}}

ln (\frac{5}{3})

3 x - 6 + 4 = - 20

\frac{( \frac{4 x ^{- 2}}{9 x ^{2}} ) ^{\frac{- 1}{2}}}{( \frac{8 x ^{3}}{27 y ^{3}} ) ^{\frac{- 1}{3}}}

10 \times \frac{38}{5}

32 + 3