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Popular >

simplify (2a^2*sqrt(2))^{3/2}

Solution

simplify

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

Solution

4 \cdot 2^{\frac{1}{4}} a^{3}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(a^{2})^{\frac{3}{2}} : a^{3}

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

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

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

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

= 2 \cdot 2^{\frac{1}{2}} \cdot 2^{\frac{3}{4}} a^{3}

Apply exponent rule:

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

2 \cdot 2^{\frac{1}{2}} \cdot 2^{\frac{3}{4}} = 2^{1 + \frac{1}{2} + \frac{3}{4}}

= a^{3} \cdot 2^{1 + \frac{1}{2} + \frac{3}{4}}

2^{1 + \frac{1}{2} + \frac{3}{4}} = 2^{2} \cdot 2^{\frac{1}{4}}

= 2^{2} \cdot 2^{\frac{1}{4}} a^{3}

2^{2} = 4

= 4 \cdot 2^{\frac{1}{4}} a^{3}

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Frequently Asked Questions (FAQ)

What is (2a^2*sqrt(2))^{3/2} ?
The solution to (2a^2*sqrt(2))^{3/2} is 4*2^{1/4}a^3