The expression sqrt(3^(5))*sqrt(3^(5)) is equivalent to 3^((1)/(5)) 3^((25)/(4)) 3^((4)/(25)) 3^(5)

Understand the problem: Understand the problem. We need to simplify the expression sqrt(3^(5))*sqrt(3^(5)).Apply property of square roots: Apply the property of square roots. The square root of a number raised to a power is the same as that number raised to half the power. So, sqrt(3^(5)) is the same as 3^(5/2).Multiply the expressions: Multiply the expressions. Now we multiply 3^(5/2) by 3^(5/2). When multiplying expressions with the same base, we add the exponents. 3^(5/2) * 3^(5/2) = 3^((5/2) + (5/2))Add the exponents: Add the exponents. (5/2) + (5/2) = 10/2Simplify the exponent: Simplify the exponent. 10/2 = 5 So, 3^(5/2) * 3^(5/2) = 3^5Write final answer: Write the final answer. The expression sqrt(3^(5))*sqrt(3^(5)) is equivalent to 3^5.

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The expression
sqrt(3^(5))*sqrt(3^(5)) is equivalent to

3^((1)/(5))

3^((25)/(4))

3^((4)/(25))

3^(5)

The expression $\sqrt{3^{5}} \cdot \sqrt{3^{5}}$ is equivalent to $\newline$ $3^{\frac{1}{5}}$ $\newline$ $3^{\frac{25}{4}}$ $\newline$ $3^{\frac{4}{25}}$ $\newline$ $3^{5}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt{3^{5}} \cdot \sqrt{3^{5}}

is equivalent to

\newline

3^{\frac{1}{5}}

\newline

3^{\frac{25}{4}}

\newline

3^{\frac{4}{25}}

\newline

3^{5}

Understand the problem: Understand the problem. $\newline$ We need to simplify the expression $\sqrt{3^{5}}$ $\sqrt{3^{5}}$ .
Apply property of square roots: Apply the property of square roots. The square root of a number raised to a power is the same as that number raised to half the power. So, $\sqrt{3^{5}}$ is the same as $3^{\frac{5}{2}}$ .
Multiply the expressions: Multiply the expressions. $\newline$ Now we multiply $3^{\frac{5}{2}}$ by $3^{\frac{5}{2}}$ . When multiplying expressions with the same base, we add the exponents. $\newline$ $3^{\frac{5}{2}} \times 3^{\frac{5}{2}} = 3^{(\frac{5}{2} + \frac{5}{2})}$
Add the exponents: Add the exponents. $\newline$ $(\frac{5}{2}) + (\frac{5}{2}) = \frac{10}{2}$
Simplify the exponent: Simplify the exponent. $\newline$ $\frac{10}{2} = 5$ $\newline$ So, $3^{\frac{5}{2}} \times 3^{\frac{5}{2}} = 3^5$
Write final answer: Write the final answer. $\newline$ The expression $\sqrt{3^{5}}$ $\sqrt{3^{5}}$ is equivalent to $3^{5}$ .