Question

question
select the expression that is equivalent to (sqrt5{54} cdot sqrt3{55}).
answer
(5^{\frac{15}{37}}) (circ)
(5^{\frac{3}{54}}) (circ)
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Explanation:

Step1: Convert roots to exponents

$\sqrt[5]{5^4} = 5^{\frac{4}{5}}$, $\sqrt[3]{5^5} = 5^{\frac{5}{3}}$

Step2: Multiply using exponent rule

When multiplying like bases, add exponents: $5^{\frac{4}{5}} \cdot 5^{\frac{5}{3}} = 5^{\frac{4}{5}+\frac{5}{3}}$

Step3: Add the fractions

Find common denominator (15): $\frac{4}{5}+\frac{5}{3} = \frac{12}{15}+\frac{25}{15} = \frac{37}{15}$

Answer:

$5^{\frac{37}{15}}$

(Note: Based on the calculation, the correct equivalent expression is $5^{\frac{37}{15}}$, which is the reverse of the first listed option. This suggests a possible typo in the provided answer choices, as the calculated result matches the inverse of the first option shown.)