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Popular >

simplify (4x^2)^{3/2}

Solution

simplify

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

Solution

8 x^{3}

Solution steps

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

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

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

= 8 x^{3}

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Frequently Asked Questions (FAQ)

What is (4x^2)^{3/2} ?
The solution to (4x^2)^{3/2} is 8x^3