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Popular >

simplify (8)^{3/2}

Solution

simplify

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

Solution

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

+1

Decimal Notation

22.62741 \dots

Solution steps

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

Prime factorization of

8 : 2^{3}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

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

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

Multiply the numbers:

8 \cdot 2 = 16

= 16 \cdot 2^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is (8)^{3/2} ?
The solution to (8)^{3/2} is 16*2^{1/2}