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Popular >

simplify 24^{3/2}

Solution

simplify

2 4^{\frac{3}{2}}

Solution

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

+1

Decimal Notation

117.57550 \dots

Solution steps

2 4^{\frac{3}{2}}

Prime factorization of

24 : 2^{3} \cdot 3

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

(2 \cdot 3)^{\frac{3}{2}} = 6 \cdot 6^{\frac{1}{2}}

= 8 \cdot 6 \cdot 6^{\frac{1}{2}}

Multiply the numbers:

8 \cdot 6 = 48

= 48 \cdot 6^{\frac{1}{2}}

Popular Examples

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12 y^{2} - 58 y - 70

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∣ 9 x + 2 ∣ + 4 < 6

Frequently Asked Questions (FAQ)

What is 24^{3/2} ?
The solution to 24^{3/2} is 48*6^{1/2}