The expression root(6)(5)*root(5)(5) is equivalent to 25^((11)/(30)) 25^((1)/(30)) 5^((1)/(30)) 5^((11)/(30))

Understand the expression: Understand the given expression. We have the expression root(6)(5)*root(5)(5), which means the 6th root of 5 multiplied by the 5th root of 5.Convert to fractional exponents: Convert the roots to fractional exponents. The 6th root of 5 can be written as 5^(1/6), and the 5th root of 5 can be written as 5^(1/5). So, root(6)(5)*root(5)(5) becomes 5^(1/6) * 5^(1/5).Apply multiplication rule: Apply the rule for multiplying powers with the same base. When multiplying powers with the same base, we add the exponents. So, 5^(1/6) * 5^(1/5) = 5^(1/6 + 1/5).Find common denominator: Find a common denominator and add the exponents. The common denominator for 6 and 5 is 30. So, 1/6 + 1/5 = 5/30 + 6/30 = 11/30. Therefore, 5^(1/6 + 1/5) = 5^(11/30).Write final answer: Write the final answer. The equivalent expression for root(6)(5)*root(5)(5) is 5^(11/30).

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The expression
root(6)(5)*root(5)(5) is equivalent to

25^((11)/(30))

25^((1)/(30))

5^((1)/(30))

5^((11)/(30))

The expression $\sqrt[6]{5} \cdot \sqrt[5]{5}$ is equivalent to $\newline$ $25^{\frac{11}{30}}$ $\newline$ $25^{\frac{1}{30}}$ $\newline$ $5^{\frac{1}{30}}$ $\newline$ $5^{\frac{11}{30}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt[6]{5} \cdot \sqrt[5]{5}

is equivalent to

\newline

25^{\frac{11}{30}}

\newline

25^{\frac{1}{30}}

\newline

5^{\frac{1}{30}}

\newline

5^{\frac{11}{30}}

Understand the expression: Understand the given expression. $\newline$ We have the expression $\sqrt[6]{5}\cdot\sqrt[5]{5}$ , which means the $6$ th root of $5$ multiplied by the $5$ th root of $5$ .
Convert to fractional exponents: Convert the roots to fractional exponents. $\newline$ The $6^{\text{th}}$ root of $5$ can be written as $5^{(1/6)}$ , and the $5^{\text{th}}$ root of $5$ can be written as $5^{(1/5)}$ . $\newline$ So, $\sqrt[6]{5}\cdot\sqrt[5]{5}$ becomes $5^{(1/6)} \cdot 5^{(1/5)}$ .
Apply multiplication rule: Apply the rule for multiplying powers with the same base. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ So, $5^{1/6} \times 5^{1/5} = 5^{1/6 + 1/5}$ .
Find common denominator: Find a common denominator and add the exponents. $\newline$ The common denominator for $6$ and $5$ is $30$ . $\newline$ So, $\frac{1}{6} + \frac{1}{5} = \frac{5}{30} + \frac{6}{30} = \frac{11}{30}$ . $\newline$ Therefore, $5^{\frac{1}{6} + \frac{1}{5}} = 5^{\frac{11}{30}}$ .
Write final answer: Write the final answer. $\newline$ The equivalent expression for $\sqrt[6]{5}\cdot\sqrt[5]{5}$ is $5^{\frac{11}{30}}$ .