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Popular >

simplify 2^{5/4}*3^{5/4}

Solution

simplify

2^{\frac{5}{4}} \cdot 3^{\frac{5}{4}}

Solution

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

+1

Solution steps

2^{\frac{5}{4}} \cdot 3^{\frac{5}{4}}

Apply exponent rule:

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

2^{\frac{5}{4}} \cdot 3^{\frac{5}{4}} = (2 \cdot 3)^{\frac{5}{4}}

= (2 \cdot 3)^{\frac{5}{4}}

Multiply the numbers:

2 \cdot 3 = 6

= 6^{\frac{5}{4}}

6^{\frac{5}{4}} = 6^{1 + \frac{1}{4}}

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

Apply exponent rule:

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

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

Refine

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

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Frequently Asked Questions (FAQ)

What is 2^{5/4}*3^{5/4} ?
The solution to 2^{5/4}*3^{5/4} is 6*6^{1/4}