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Popular >

simplify 27^{3/2}

Solution

simplify

2 7^{\frac{3}{2}}

Solution

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

+1

Decimal

140.29611 \dots

Solution steps

2 7^{\frac{3}{2}}

Prime factorization of

27 : 3^{3}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

(3^{2})^{\frac{3}{2}} = 27

= 27 \cdot 3^{\frac{3}{2}}

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

= 27 \cdot 3 \cdot 3^{\frac{1}{2}}

Multiply the numbers:

27 \cdot 3 = 81

= 81 \cdot 3^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is 27^{3/2} ?
The solution to 27^{3/2} is 81*3^{1/2}