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Popular >

simplify (4x^2)^{5/2}

Solution

simplify

(4 x^{2})^{\frac{5}{2}}

Solution

32 x^{5}

Solution steps

(4 x^{2})^{\frac{5}{2}}

Apply exponent rule:

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

(4 x^{2})^{\frac{5}{2}} = 4^{\frac{5}{2}} (x^{2})^{\frac{5}{2}}

= 4^{\frac{5}{2}} (x^{2})^{\frac{5}{2}}

4^{\frac{5}{2}} = 32

= 32 (x^{2})^{\frac{5}{2}}

Apply exponent rule:

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

assuming

a \geq 0

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

= 32 x^{2 \cdot \frac{5}{2}}

2 \cdot \frac{5}{2} = 5

= 32 x^{5}

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Frequently Asked Questions (FAQ)

What is (4x^2)^{5/2} ?
The solution to (4x^2)^{5/2} is 32x^5