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Popular >

simplify 40^{3/2}

Solution

simplify

4 0^{\frac{3}{2}}

Solution

80 \cdot 1 0^{\frac{1}{2}}

+1

Decimal Notation

252.98221 \dots

Solution steps

4 0^{\frac{3}{2}}

Prime factorization of

40 : 2^{3} \cdot 5

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

Apply exponent rule:

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

2^{3} \cdot 5 = 2^{2} \cdot 2 \cdot 5

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

Apply exponent rule:

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

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

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

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

= 8 (2 \cdot 5)^{\frac{3}{2}}

(2 \cdot 5)^{\frac{3}{2}} = 10 \cdot 1 0^{\frac{1}{2}}

= 8 \cdot 10 \cdot 1 0^{\frac{1}{2}}

Multiply the numbers:

8 \cdot 10 = 80

= 80 \cdot 1 0^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is 40^{3/2} ?
The solution to 40^{3/2} is 80*10^{1/2}