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Popular >

simplify (16sqrt(x^3))^{1/4}

Solution

simplify

(16 x^{3})^{\frac{1}{4}}

Solution

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

Solution steps

(16 x^{3})^{\frac{1}{4}}

Apply exponent rule:

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

(16 x^{3})^{\frac{1}{4}} = 1 6^{\frac{1}{4}} (x^{3})^{\frac{1}{4}}

= 1 6^{\frac{1}{4}} (x^{3})^{\frac{1}{4}}

1 6^{\frac{1}{4}} = 2

= 2 (x^{3})^{\frac{1}{4}}

Simplify

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

= 2 (x^{\frac{3}{2}})^{\frac{1}{4}}

Apply exponent rule:

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

assuming

a \geq 0

(x^{\frac{3}{2}})^{\frac{1}{4}} = x^{\frac{3}{2} \cdot \frac{1}{4}}

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

\frac{3}{2} \cdot \frac{1}{4} = \frac{3}{8}

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

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Frequently Asked Questions (FAQ)

What is (16sqrt(x^3))^{1/4} ?
The solution to (16sqrt(x^3))^{1/4} is 2x^{3/8}