What is 3^{1/4}\times 27^{1/4} ?

The solution to 3^{1/4}\times 27^{1/4} is 3

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simplify 3^{1/4}\times 27^{1/4}

simplify

3^{\frac{1}{4}} \cdot 2 7^{\frac{1}{4}}

3

Solution steps

3^{\frac{1}{4}} \cdot 2 7^{\frac{1}{4}}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

3^{\frac{1}{4}} \cdot 2 7^{\frac{1}{4}} = (3 \cdot 27)^{\frac{1}{4}}

= (3 \cdot 27)^{\frac{1}{4}}

Multiply the numbers:

3 \cdot 27 = 81

= 8 1^{\frac{1}{4}}

Factor the number:

81 = 3^{4}

= (3^{4})^{\frac{1}{4}}

Apply exponent rule:

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

(3^{4})^{\frac{1}{4}} = 3^{4 \cdot \frac{1}{4}} = 3

= 3

- 7 e^{- l n (7)}

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

e^{3 x} \times e^{- 4 x}

e^{6 x} e^{x}