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Popular >

simplify 243^{1/3}*3^{1/3}

Solution

simplify

24 3^{\frac{1}{3}} \cdot 3^{\frac{1}{3}}

Solution

9

Solution steps

24 3^{\frac{1}{3}} \cdot 3^{\frac{1}{3}}

24 3^{\frac{1}{3}} = 3 \cdot 3^{\frac{2}{3}}

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

Apply exponent rule:

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

3^{\frac{2}{3}} \cdot 3^{\frac{1}{3}} = 3^{\frac{2}{3} + \frac{1}{3}}

= 3 \cdot 3^{\frac{2}{3} + \frac{1}{3}}

\frac{2}{3} + \frac{1}{3} = 1

= 3 \cdot 3^{1}

Apply exponent rule:

a^{1} = a

3^{1} = 3

= 3 \cdot 3

Apply exponent rule:

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

3 \cdot 3 = 3^{1 + 1}

= 3^{1 + 1}

Add the numbers:

1 + 1 = 2

= 3^{2}

3^{2} = 9

= 9

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Frequently Asked Questions (FAQ)

What is 243^{1/3}*3^{1/3} ?
The solution to 243^{1/3}*3^{1/3} is 9