Write root(4)(7)*sqrt49 using rational exponents. A. 4^((5)/(7)) B. 7^((5)/(4)) C. 4^(7) D. 7^(4)

Convert to Rational Exponents: Convert the fourth root and the square root to rational exponents. The fourth root of 7 can be written as 7^(1/4), and the square root of 49 can be written as 49^(1/2).Simplify Square Root: Simplify the square root of 49. Since 49 is a perfect square, 49^(1/2) is equal to 7. So, we have 7^(1/4) * 7.Write 7 as Power: Write 7 as a power of 7 with an exponent of 1. 7 can be written as 7^(1). So, we have 7^(1/4) * 7^(1).Combine Exponents: Use the property of exponents to combine the terms. When multiplying with the same base, add the exponents: 7^(1/4) * 7^(1) = 7^(1/4 + 1).Add Exponents: Add the exponents. 1/4 + 1 is the same as 1/4 + 4/4, which equals 5/4. So, we have 7^(5/4).Match with Options: Match the result with the given options. The expression 7^(5/4) matches option B.

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Write
root(4)(7)*sqrt49 using rational exponents.
A.
4^((5)/(7))
B.
7^((5)/(4))
C.
4^(7)
D.
7^(4)

Write $\sqrt[4]{7} \cdot \sqrt{49}$ using rational exponents. $\newline$ A. $4^{\frac{5}{7}}$ $\newline$ B. $7^{\frac{5}{4}}$ $\newline$ C. $4^{7}$ $\newline$ D. $7^{4}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Write

\sqrt[4]{7} \cdot \sqrt{49}

using rational exponents.

\newline

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

\newline

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

\newline

4^{7}

\newline

7^{4}

Convert to Rational Exponents: Convert the fourth root and the square root to rational exponents. $\newline$ The fourth root of $7$ can be written as $7^{1/4}$ , and the square root of $49$ can be written as $49^{1/2}$ .
Simplify Square Root: Simplify the square root of $49$ . $\newline$ Since $49$ is a perfect square, $49^{(1/2)}$ is equal to $7$ . $\newline$ So, we have $7^{(1/4)} \times 7$ .
Write $7$ as Power: Write $7$ as a power of $7$ with an exponent of $1$ . $7$ can be written as $7^{1}$ . So, we have $7^{1/4} \times 7^{1}$ .
Combine Exponents: Use the property of exponents to combine the terms. $\newline$ When multiplying with the same base, add the exponents: $7^{1/4} \times 7^{1} = 7^{1/4 + 1}$ .
Add Exponents: Add the exponents. $\newline$ $\frac{1}{4} + 1$ is the same as $\frac{1}{4} + \frac{4}{4}$ , which equals $\frac{5}{4}$ . $\newline$ So, we have $7^{\frac{5}{4}}$ .
Match with Options: Match the result with the given options. $\newline$ The expression $7^{5/4}$ matches option $B$ .