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Popular >

simplify 3^33^{1/2}3^{2/3}

Solution

simplify

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

Solution

81 \cdot 3^{\frac{1}{6}}

+1

Decimal Notation

97.27589 \dots

Solution steps

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

Apply exponent rule:

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

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

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

3 + \frac{1}{2} + \frac{2}{3} = \frac{25}{6}

= 3^{\frac{25}{6}}

3^{\frac{25}{6}} = 3^{4 + \frac{1}{6}}

= 3^{4 + \frac{1}{6}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 3^{4} \cdot 3^{\frac{1}{6}}

3^{4} = 81

= 81 \cdot 3^{\frac{1}{6}}

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Frequently Asked Questions (FAQ)

What is 3^33^{1/2}3^{2/3} ?
The solution to 3^33^{1/2}3^{2/3} is 81*3^{1/6}