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Popular >

simplify 2(12)^{3/2}

Solution

simplify

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

Solution

3^{\frac{1}{2}} \cdot 48

+1

Solution steps

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

Prime factorization of

12 : 2^{2} \cdot 3

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

Apply exponent rule:

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

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

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

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

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

8 \cdot 3^{\frac{3}{2}} = 24 \cdot 3^{\frac{1}{2}}

= 2 \cdot 24 \cdot 3^{\frac{1}{2}}

Multiply the numbers:

2 \cdot 24 = 48

= 48 \cdot 3^{\frac{1}{2}}

= 3^{\frac{1}{2}} \cdot 48

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Frequently Asked Questions (FAQ)

What is 2(12)^{3/2} ?
The solution to 2(12)^{3/2} is 3^{1/2}*48