The expression root(4)(7)*root(4)(7) is equivalent to 49^((1)/(16)) 49^((1)/(2)) 7^((1)/(16)) 7^((1)/(2))

Understand the problem: Understand the problem. We need to find the equivalent expression for the product of two fourth roots of 7.Use property of exponents: Use the property of exponents for roots. The fourth root of a number can be written as that number raised to the 1/4 power. So, root(4)(7) can be written as 7^(1/4).Multiply the expressions: Multiply the expressions. We have 7^(1/4) * 7^(1/4). When multiplying expressions with the same base, we add the exponents.Add the exponents: Add the exponents. 7^(1/4) * 7^(1/4) = 7^(1/4 + 1/4) = 7^(2/4)Simplify the exponent: Simplify the exponent. 7^(2/4) simplifies to 7^(1/2), because 2/4 reduces to 1/2.Write the final answer: Write the final answer. The equivalent expression for root(4)(7)*root(4)(7) is 7^(1/2).

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The expression
root(4)(7)*root(4)(7) is equivalent to

49^((1)/(16))

49^((1)/(2))

7^((1)/(16))

7^((1)/(2))

The expression $\sqrt[4]{7} \cdot \sqrt[4]{7}$ is equivalent to $\newline$ $49^{\frac{1}{16}}$ $\newline$ $49^{\frac{1}{2}}$ $\newline$ $7^{\frac{1}{16}}$ $\newline$ $7^{\frac{1}{2}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt[4]{7} \cdot \sqrt[4]{7}

is equivalent to

\newline

49^{\frac{1}{16}}

\newline

49^{\frac{1}{2}}

\newline

7^{\frac{1}{16}}

\newline

7^{\frac{1}{2}}

Understand the problem: Understand the problem. We need to find the equivalent expression for the product of two fourth roots of $7$ .
Use property of exponents: Use the property of exponents for roots. $\newline$ The fourth root of a number can be written as that number raised to the $1/4$ power. So, $\sqrt[4]{7}$ can be written as $7^{1/4}$ .
Multiply the expressions: Multiply the expressions. $\newline$ We have $7^{1/4} \times 7^{1/4}$ . When multiplying expressions with the same base, we add the exponents.
Add the exponents: Add the exponents. $7^{\frac{1}{4}} \times 7^{\frac{1}{4}} = 7^{\frac{1}{4} + \frac{1}{4}} = 7^{\frac{2}{4}}$
Simplify the exponent: Simplify the exponent. $7^{\frac{2}{4}}$ simplifies to $7^{\frac{1}{2}}$ , because $\frac{2}{4}$ reduces to $\frac{1}{2}$ .
Write the final answer: Write the final answer. $\newline$ The equivalent expression for $\sqrt[4]{7}\times\sqrt[4]{7}$ is $7^{1/2}$ .