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Popular >

simplify 32^{3/2}

Solution

simplify

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

Solution

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

+1

Decimal Notation

181.01933 \dots

Solution steps

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

Prime factorization of

32 : 2^{5}

= (2^{5})^{\frac{3}{2}}

Apply exponent rule:

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

2^{5} = 2^{4} \cdot 2

= (2^{4} \cdot 2)^{\frac{3}{2}}

Apply exponent rule:

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

(2^{4} \cdot 2)^{\frac{3}{2}} = (2^{4})^{\frac{3}{2}} \cdot 2^{\frac{3}{2}}

= (2^{4})^{\frac{3}{2}} \cdot 2^{\frac{3}{2}}

(2^{4})^{\frac{3}{2}} = 64

= 64 \cdot 2^{\frac{3}{2}}

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

= 64 \cdot 2 \cdot 2^{\frac{1}{2}}

Multiply the numbers:

64 \cdot 2 = 128

= 128 \cdot 2^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is 32^{3/2} ?
The solution to 32^{3/2} is 128*2^{1/2}