The expression root(3)(2^(2))*root(3)(2) is equivalent to 4^((2)/(9)) 2^((2)/(9)) 2 4

Understand the expression: Understand the given expression. We have the expression root(3)(2^(2))*root(3)(2), which means we are multiplying two cube roots together. The first cube root is of 2 squared, and the second is just of 2.Use property of exponents: Use the property of exponents for roots. The cube root of a number can be written as that number raised to the power of 1/3. So we can rewrite the expression as: (2^2)^(1/3) * 2^(1/3)Apply power to power rule: Apply the power to a power rule. When you raise a power to another power, you multiply the exponents. So we can simplify the first term as follows: (2^(2*1/3)) * 2^(1/3) = 2^(2/3) * 2^(1/3)Combine terms with same base: Combine the terms with the same base. When multiplying terms with the same base, you add the exponents. So we add the exponents 2/3 and 1/3: 2^(2/3 + 1/3) = 2^(3/3)Simplify the exponent: Simplify the exponent. Since 3/3 equals 1, we simplify the expression to: 2^1 Which is simply 2.Check final answer: Check the final answer against the given options. The final simplified expression is 2, which matches one of the given options.

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The expression
root(3)(2^(2))*root(3)(2) is equivalent to

4^((2)/(9))

2^((2)/(9))
2
4

The expression $\sqrt[3]{2^{2}} \cdot \sqrt[3]{2}$ is equivalent to $\newline$ $4^{\frac{2}{9}}$ $\newline$ $2^{\frac{2}{9}}$ $\newline$ $2$ $\newline$ $4$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt[3]{2^{2}} \cdot \sqrt[3]{2}

is equivalent to

\newline

4^{\frac{2}{9}}

\newline

2^{\frac{2}{9}}

\newline

2

\newline

4

Understand the expression: Understand the given expression. $\newline$ We have the expression $\sqrt[3]{2^{2}}\cdot\sqrt[3]{2}$ , which means we are multiplying two cube roots together. The first cube root is of $2$ squared, and the second is just of $2$ .
Use property of exponents: Use the property of exponents for roots. $\newline$ The cube root of a number can be written as that number raised to the power of $\frac{1}{3}$ . So we can rewrite the expression as: $\newline$ $(2^2)^{\frac{1}{3}} \times 2^{\frac{1}{3}}$
Apply power to power rule: Apply the power to a power rule. $\newline$ When you raise a power to another power, you multiply the exponents. So we can simplify the first term as follows: $\newline$ $(2^{2\cdot\frac{1}{3}}) \cdot 2^{\frac{1}{3}}$ $\newline$ = $2^{\frac{2}{3}} \cdot 2^{\frac{1}{3}}$
Combine terms with same base: Combine the terms with the same base. $\newline$ When multiplying terms with the same base, you add the exponents. So we add the exponents $\frac{2}{3}$ and $\frac{1}{3}$ : $\newline$ $2^{\frac{2}{3} + \frac{1}{3}}$ $\newline$ = $2^{\frac{3}{3}}$
Simplify the exponent: Simplify the exponent. $\newline$ Since $\frac{3}{3}$ equals $1$ , we simplify the expression to: $\newline$ $2^1$ $\newline$ Which is simply $2$ .
Check final answer: Check the final answer against the given options. $\newline$ The final simplified expression is $2$ , which matches one of the given options.