The expression root(4)(7^(3))*root(3)(7) is equivalent to 7^((13)/(12)) 7^((1)/(4)) 49^((13)/(12)) 49^((1)/(4))

Rewrite using Exponent Notation: We are given the expression root(4)(7^(3))*root(3)(7) and we need to simplify it. The fourth root of 7^3 can be written as 7^(3/4), and the cube root of 7 can be written as 7^(1/3). So, we rewrite the expression using exponent notation.Add Exponents with Same Base: Now we have 7^(3/4) * 7^(1/3). To multiply two exponents with the same base, we add the exponents. So, we add 3/4 and 1/3.Find Common Denominator: To add the fractions 3/4 and 1/3, we need a common denominator. The least common denominator for 4 and 3 is 12. We convert each fraction to have a denominator of 12: (3/4)*(12/12) = 9/12 and (1/3)*(12/12) = 4/12.Combine Exponents: Now we add the two fractions: 9/12 + 4/12 = 13/12. So, the combined exponent for 7 is 13/12. We write the simplified expression as 7^(13/12).Check Answer Choices: We check the answer choices to see which one matches our simplified expression. The correct answer is 7^((13)/(12)).

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The expression
root(4)(7^(3))*root(3)(7) is equivalent to

7^((13)/(12))

7^((1)/(4))

49^((13)/(12))

49^((1)/(4))

The expression $\sqrt[4]{7^{3}} \cdot \sqrt[3]{7}$ is equivalent to $\newline$ $7^{\frac{13}{12}}$ $\newline$ $7^{\frac{1}{4}}$ $\newline$ $49^{\frac{13}{12}}$ $\newline$ $49^{\frac{1}{4}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt[4]{7^{3}} \cdot \sqrt[3]{7}

is equivalent to

\newline

7^{\frac{13}{12}}

\newline

7^{\frac{1}{4}}

\newline

49^{\frac{13}{12}}

\newline

49^{\frac{1}{4}}

Rewrite using Exponent Notation: We are given the expression $\sqrt[4]{7^{3}}\cdot\sqrt[3]{7}$ and we need to simplify it. The fourth root of $7^3$ can be written as $7^{\frac{3}{4}}$ , and the cube root of $7$ can be written as $7^{\frac{1}{3}}$ . So, we rewrite the expression using exponent notation.
Add Exponents with Same Base: Now we have $7^{\frac{3}{4}} \times 7^{\frac{1}{3}}$ . To multiply two exponents with the same base, we add the exponents. So, we add $\frac{3}{4}$ and $\frac{1}{3}$ .
Find Common Denominator: To add the fractions $\frac{3}{4}$ and $\frac{1}{3}$ , we need a common denominator. The least common denominator for $4$ and $3$ is $12$ . We convert each fraction to have a denominator of $12$ : $\left(\frac{3}{4}\right)\left(\frac{12}{12}\right) = \frac{9}{12}$ and $\left(\frac{1}{3}\right)\left(\frac{12}{12}\right) = \frac{4}{12}$ .
Combine Exponents: Now we add the two fractions: $\frac{9}{12} + \frac{4}{12} = \frac{13}{12}$ . So, the combined exponent for $7$ is $\frac{13}{12}$ . We write the simplified expression as $7^{\frac{13}{12}}$ .
Check Answer Choices: We check the answer choices to see which one matches our simplified expression. The correct answer is $7^{(13/12)}$ .