The expression root(4)(3)*sqrt3 is equivalent to 3^((4)/(3)) 3^(8) 3^((1)/(8)) 3^((3)/(4))

Given Expression: We are given the expression root(4)(3) * sqrt(3), which means we have a fourth root of 3 multiplied by a square root of 3. We need to express this in terms of a single power of 3.Express in Terms: The fourth root of 3 can be written as 3^(1/4), and the square root of 3 can be written as 3^(1/2). So, root(4)(3) * sqrt(3) = 3^(1/4) * 3^(1/2).Add Exponents: When multiplying expressions with the same base, we add the exponents. So, we add 1/4 and 1/2 to get the new exponent for 3. 1/4 + 1/2 = 1/4 + 2/4 = 3/4. Therefore, 3^(1/4) * 3^(1/2) = 3^(3/4).Final Simplified Form: Now we have the expression in the form of a single power of 3, which is 3^(3/4). This is the simplified form of the original expression.

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The expression
root(4)(3)*sqrt3 is equivalent to

3^((4)/(3))

3^(8)

3^((1)/(8))

3^((3)/(4))

The expression $\sqrt[4]{3} \cdot \sqrt{3}$ is equivalent to $\newline$ $3^{\frac{4}{3}}$ $\newline$ $3^{8}$ $\newline$ $3^{\frac{1}{8}}$ $\newline$ $3^{\frac{3}{4}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. The expression

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

is equivalent to

\newline

3^{\frac{4}{3}}

\newline

3^{8}

\newline

3^{\frac{1}{8}}

\newline

3^{\frac{3}{4}}

Given Expression: We are given the expression $\sqrt[4]{3} \times \sqrt{3}$ , which means we have a fourth root of $3$ multiplied by a square root of $3$ . We need to express this in terms of a single power of $3$ .
Express in Terms: The fourth root of $3$ can be written as $3^{1/4}$ , and the square root of $3$ can be written as $3^{1/2}$ . $\newline$ So, $\sqrt[4]{3} \times \sqrt{3} = 3^{1/4} \times 3^{1/2}$ .
Add Exponents: When multiplying expressions with the same base, we add the exponents. So, we add $\frac{1}{4}$ and $\frac{1}{2}$ to get the new exponent for $3$ . $\newline$ $\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ . $\newline$ Therefore, $3^{\frac{1}{4}} \times 3^{\frac{1}{2}} = 3^{\frac{3}{4}}$ .
Final Simplified Form: Now we have the expression in the form of a single power of $3$ , which is $3^{\frac{3}{4}}$ . This is the simplified form of the original expression.