The expression root(5)(10^(2))*root(5)(10^(2)) is equivalent to 10^((4)/(25)) 10^((25)/(4)) 10^((5)/(4)) 10^((4)/(5))

Understand the Problem: Understand the problem. We need to simplify the expression involving the fifth root of 10 squared, multiplied by itself.Use Exponent Property: Use the property of exponents for roots. The fifth root of 10 squared can be written as 10^(2/5). So, root(5)(10^(2)) * root(5)(10^(2)) becomes 10^(2/5) * 10^(2/5).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, 10^(2/5) * 10^(2/5) = 10^((2/5) + (2/5)).Perform Exponent Addition: Perform the addition of the exponents. (2/5) + (2/5) = 4/5. So, 10^(2/5) * 10^(2/5) = 10^(4/5).

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The expression
root(5)(10^(2))*root(5)(10^(2)) is equivalent to

10^((4)/(25))

10^((25)/(4))

10^((5)/(4))

10^((4)/(5))

The expression $\sqrt[5]{10^{2}} \cdot \sqrt[5]{10^{2}}$ is equivalent to $\newline$ $10^{\frac{4}{25}}$ $\newline$ $10^{\frac{25}{4}}$ $\newline$ $10^{\frac{5}{4}}$ $\newline$ $10^{\frac{4}{5}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt[5]{10^{2}} \cdot \sqrt[5]{10^{2}}

is equivalent to

\newline

10^{\frac{4}{25}}

\newline

10^{\frac{25}{4}}

\newline

10^{\frac{5}{4}}

\newline

10^{\frac{4}{5}}

Understand the Problem: Understand the problem. We need to simplify the expression involving the fifth root of $10$ squared, multiplied by itself.
Use Exponent Property: Use the property of exponents for roots. $\newline$ The fifth root of $10^2$ squared can be written as $10^{(2/5)}$ . $\newline$ So, $\sqrt[5]{10^2} \times \sqrt[5]{10^2}$ becomes $10^{(2/5)} \times 10^{(2/5)}$ .
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, $10^{\frac{2}{5}} \times 10^{\frac{2}{5}} = 10^{(\frac{2}{5} + \frac{2}{5})}.$
Perform Exponent Addition: Perform the addition of the exponents. $\newline$ $(\frac{2}{5}) + (\frac{2}{5}) = \frac{4}{5}$ . $\newline$ So, $10^{(\frac{2}{5})} \times 10^{(\frac{2}{5})} = 10^{(\frac{4}{5})}$ .