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Popular >

simplify (27x^3)^{4/3}

Solution

simplify

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

Solution

81 x^{4}

Solution steps

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

Apply exponent rule:

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

(27 x^{3})^{\frac{4}{3}} = 2 7^{\frac{4}{3}} (x^{3})^{\frac{4}{3}}

= 2 7^{\frac{4}{3}} (x^{3})^{\frac{4}{3}}

2 7^{\frac{4}{3}} = 81

= 81 (x^{3})^{\frac{4}{3}}

Apply exponent rule:

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

assuming

a \geq 0

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

= 81 x^{3 \cdot \frac{4}{3}}

3 \cdot \frac{4}{3} = 4

= 81 x^{4}

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Frequently Asked Questions (FAQ)

What is (27x^3)^{4/3} ?
The solution to (27x^3)^{4/3} is 81x^4