The expression root(5)(7^(2))*root(5)(7^(2)) is equivalent to 7^((4)/(5)) 49^((4)/(5)) 7^((4)/(25)) 49^((4)/(25))

Understand the problem: Understand the problem. We need to simplify the expression root(5)(7^(2))*root(5)(7^(2)). This involves two fifth roots of 7 squared being multiplied together.Use property of exponents: 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, root(5)(7^(2)) is the same as (7^(2))^(1/5).Apply power of power rule: Apply the power of a power rule. When you raise a power to a power, you multiply the exponents. So, (7^(2))^(1/5) becomes 7^(2*(1/5)), which simplifies to 7^(2/5).Multiply the expressions: Multiply the expressions. Now we multiply 7^(2/5) by itself: 7^(2/5) * 7^(2/5).Apply product of powers rule: Apply the product of powers rule. When you multiply powers with the same base, you add the exponents. So, 7^(2/5) * 7^(2/5) becomes 7^((2/5) + (2/5)), which simplifies to 7^(4/5).Check answer choices: Check the answer choices. We have simplified the expression to 7^(4/5). Now we compare this with the given answer choices.Select correct answer: Select the correct answer. The correct answer is 7^((4)/(5)), which matches one of the given answer choices.

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The expression
root(5)(7^(2))*root(5)(7^(2)) is equivalent to

7^((4)/(5))

49^((4)/(5))

7^((4)/(25))

49^((4)/(25))

The expression $\sqrt[5]{7^{2}} \cdot \sqrt[5]{7^{2}}$ is equivalent to $\newline$ $7^{\frac{4}{5}}$ $\newline$ $49^{\frac{4}{5}}$ $\newline$ $7^{\frac{4}{25}}$ $\newline$ $49^{\frac{4}{25}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt[5]{7^{2}} \cdot \sqrt[5]{7^{2}}

is equivalent to

\newline

7^{\frac{4}{5}}

\newline

49^{\frac{4}{5}}

\newline

7^{\frac{4}{25}}

\newline

49^{\frac{4}{25}}

Understand the problem: Understand the problem. $\newline$ We need to simplify the expression $\sqrt[5]{7^{2}}$ $\cdot$ $\sqrt[5]{7^{2}}$ . This involves two fifth roots of $7^{2}$ being multiplied together.
Use property of exponents: 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, $\sqrt[5]{7^{2}}$ is the same as $(7^{2})^{\frac{1}{5}}$ .
Apply power of power rule: Apply the power of a power rule. $\newline$ When you raise a power to a power, you multiply the exponents. So, $(7^{2})^{\frac{1}{5}}$ becomes $7^{2*\frac{1}{5}}$ , which simplifies to $7^{\frac{2}{5}}$ .
Multiply the expressions: Multiply the expressions. $\newline$ Now we multiply $7^{2/5}$ by itself: $7^{2/5} \times 7^{2/5}$ .
Apply product of powers rule: Apply the product of powers rule. $\newline$ When you multiply powers with the same base, you add the exponents. So, $7^{2/5} \times 7^{2/5}$ becomes $7^{(2/5) + (2/5)}$ , which simplifies to $7^{4/5}$ .
Check answer choices: Check the answer choices. $\newline$ We have simplified the expression to $7^{\frac{4}{5}}$ . Now we compare this with the given answer choices.
Select correct answer: Select the correct answer. $\newline$ The correct answer is $7^{(\frac{4}{5})}$ , which matches one of the given answer choices.