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Popular >

simplify (2*6)^{3/2}

Solution

simplify

(2 \cdot 6)^{\frac{3}{2}}

Solution

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

+1

Decimal Notation

41.56921 \dots

Solution steps

(2 \cdot 6)^{\frac{3}{2}}

Apply exponent rule:

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

(2 \cdot 6)^{\frac{3}{2}} = 2^{\frac{3}{2}} \cdot 6^{\frac{3}{2}}

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

Factor integer

6 = 2 \cdot 3

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

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

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

2^{3} = 8

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

Multiply the numbers:

8 \cdot 3 = 24

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

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Frequently Asked Questions (FAQ)

What is (2*6)^{3/2} ?
The solution to (2*6)^{3/2} is 24*3^{1/2}