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Popular >

simplify \sqrt[3]{(27x^3)^4}

Solution

simplify

Solution

81 x^{4}

Solution steps

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(27 x^{3})^{3 + 1} = (27 x^{3})^{3} \cdot 27 x^{3}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply radical rule:

if

n

is odd

Simplify

= 27 x^{3} \cdot 3 x

Multiply the numbers:

27 \cdot 3 = 81

= 81 x^{3} x

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{3} x = x^{3 + 1}

= 81 x^{3 + 1}

Add the numbers:

3 + 1 = 4

= 81 x^{4}

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{(27x^3)^4} ?
The solution to \sqrt[3]{(27x^3)^4} is 81x^4