What is ((27x^5)^{1/3})/(sqrt(3x)^{1/3)} ?

The solution to ((27x^5)^{1/3})/(sqrt(3x)^{1/3)} is (3x^{5/3})/((sqrt(3x))^{1/3)}

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simplify ((27x^5)^{1/3})/(sqrt(3x)^{1/3)}

simplify

\frac{( 27 x ^{5} ) ^{\frac{1}{3}}}{3 x ^{\frac{1}{3}}}

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

Solution steps

\frac{( 27 x ^{5} ) ^{\frac{1}{3}}}{( 3 x ) ^{\frac{1}{3}}}

Apply exponent rule:

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

(27 x^{5})^{\frac{1}{3}} = 2 7^{\frac{1}{3}} (x^{5})^{\frac{1}{3}}

= \frac{2 7 ^{\frac{1}{3}} ( x ^{5} ) ^{\frac{1}{3}}}{( 3 x ) ^{\frac{1}{3}}}

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

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

5 \cdot \frac{1}{3} = \frac{5}{3}

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

3 (53)

49^{\frac{1}{2} x}

8.7 \cdot 1 0^{- 4}

e^{- 2 t} \cdot e^{- t}

5.5 \times 1 0^{- 4}

What is ((27x^5)^{1/3})/(sqrt(3x)^{1/3)} ?
The solution to ((27x^5)^{1/3})/(sqrt(3x)^{1/3)} is (3x^{5/3})/((sqrt(3x))^{1/3)}