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Popular >

simplify (25x^3)^{1/2}

Solution

simplify

(25 x^{3})^{\frac{1}{2}}

Solution

5 x^{\frac{3}{2}}

Solution steps

(25 x^{3})^{\frac{1}{2}}

Apply exponent rule:

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

(25 x^{3})^{\frac{1}{2}} = 2 5^{\frac{1}{2}} (x^{3})^{\frac{1}{2}}

= 2 5^{\frac{1}{2}} (x^{3})^{\frac{1}{2}}

2 5^{\frac{1}{2}} = 5

= 5 (x^{3})^{\frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

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

= 5 x^{3 \cdot \frac{1}{2}}

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

= 5 x^{\frac{3}{2}}

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Frequently Asked Questions (FAQ)

What is (25x^3)^{1/2} ?
The solution to (25x^3)^{1/2} is 5x^{3/2}