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Popular >

simplify (27x^3)^{1/3}

Solution

simplify

(27 x^{3})^{\frac{1}{3}}

Solution

3 x

Solution steps

(27 x^{3})^{\frac{1}{3}}

Apply exponent rule:

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

(27 x^{3})^{\frac{1}{3}} = 2 7^{\frac{1}{3}} (x^{3})^{\frac{1}{3}}

= 2 7^{\frac{1}{3}} (x^{3})^{\frac{1}{3}}

2 7^{\frac{1}{3}} = 3

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

Apply exponent rule:

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

assuming

a \geq 0

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

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

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

= 3 x^{1}

Apply exponent rule:

a^{1} = a

x^{1} = x

= 3 x

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Frequently Asked Questions (FAQ)

What is (27x^3)^{1/3} ?
The solution to (27x^3)^{1/3} is 3x