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Popular >

simplify 3^{3/4}*27^{3/4}

Solution

simplify

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

Solution

27

Solution steps

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

Apply exponent rule:

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

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

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

Multiply the numbers:

3 \cdot 27 = 81

= 8 1^{\frac{3}{4}}

Factor the number:

81 = 3^{4}

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

Apply exponent rule:

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

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

= 3^{3}

Refine

= 27

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Frequently Asked Questions (FAQ)

What is 3^{3/4}*27^{3/4} ?
The solution to 3^{3/4}*27^{3/4} is 27