What is 2^{3/2}*3^{3/2} ?

The solution to 2^{3/2}*3^{3/2} is 6*6^{1/2}

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simplify 2^{3/2}*3^{3/2}

simplify

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

6 \cdot 6^{\frac{1}{2}}

Decimal Notation

14.69693 \dots

Solution steps

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

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

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

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

Multiply the numbers:

2 \cdot 3 = 6

= 6^{\frac{3}{2}}

6^{\frac{3}{2}} = 6^{1 + \frac{1}{2}}

= 6^{1 + \frac{1}{2}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

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

Refine

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

(3 rs t^{8} u) (10 rs t u^{9})

\frac{e ^{- 3 t}}{e ^{- 4 t}}

8.69 \cdot 1 0^{6} \cdot 0.2 5^{1.75} \cdot 53. 4^{- 4.75}

9.44 \cdot 1 0^{- 6} \cdot \frac{159}{0.2 1 ^{2}}

- e^{- \frac{1}{2}}