The expression root(5)(3^(3))*root(5)(3^(3)) is equivalent to 9^((6)/(5)) 9^((9)/(25)) 3^((9)/(25)) 3^((6)/(5))

Understand Expression: Understand the given expression. We have the expression root(5)(3^(3)) * root(5)(3^(3)). This means we are multiplying two fifth roots of 3 raised to the power of 3.Use Exponent Property: Use the property of exponents for roots. The fifth root of a number is the same as raising that number to the power of 1/5. So, we can rewrite the expression as: (3^(3))^(1/5) * (3^(3))^(1/5)Apply Power Rule: Apply the power of a power rule. When we raise a power to another power, we multiply the exponents. So, we get: 3^(3*(1/5)) * 3^(3*(1/5)) = 3^(3/5) * 3^(3/5)Use Exponent Property: Use the property of exponents for multiplication. When we multiply like bases, we add the exponents. So, we get: 3^((3/5) + (3/5)) = 3^(6/5)Check for Simplification: Check if the expression can be simplified further. The expression 3^(6/5) is already in its simplest form, so we cannot simplify it further.

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

9^((6)/(5))

9^((9)/(25))

3^((9)/(25))

3^((6)/(5))

The expression $\sqrt[5]{3^{3}} \cdot \sqrt[5]{3^{3}}$ is equivalent to $\newline$ $9^{\frac{6}{5}}$ $\newline$ $9^{\frac{9}{25}}$ $\newline$ $3^{\frac{9}{25}}$ $\newline$ $3^{\frac{6}{5}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

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

is equivalent to

\newline

9^{\frac{6}{5}}

\newline

9^{\frac{9}{25}}

\newline

3^{\frac{9}{25}}

\newline

3^{\frac{6}{5}}

Understand Expression: Understand the given expression. $\newline$ We have the expression $\sqrt[5]{3^{3}} \times \sqrt[5]{3^{3}}$ . This means we are multiplying two fifth roots of $3$ raised to the power of $3$ .
Use Exponent Property: Use the property of exponents for roots. $\newline$ The fifth root of a number is the same as raising that number to the power of $\frac{1}{5}$ . So, we can rewrite the expression as: $\newline$ $(3^{3})^{\frac{1}{5}} \times (3^{3})^{\frac{1}{5}}$
Apply Power Rule: Apply the power of a power rule. $\newline$ When we raise a power to another power, we multiply the exponents. So, we get: $\newline$ $3^{3\times(1/5)} \times 3^{3\times(1/5)} = 3^{3/5} \times 3^{3/5}$
Use Exponent Property: Use the property of exponents for multiplication. $\newline$ When we multiply like bases, we add the exponents. So, we get: $\newline$ $3^{(\frac{3}{5} + \frac{3}{5})} = 3^{\frac{6}{5}}$
Check for Simplification: Check if the expression can be simplified further. $\newline$ The expression $3^{\frac{6}{5}}$ is already in its simplest form, so we cannot simplify it further.