Select the expression that is equivalent to 2x^((3)/(2)) sqrt(2x^(3)) root(3)(2x^(2)) 2root(3)(x^(2)) 2sqrt(x^(3))

Understand given expression: Understand the given expression. The given expression is 2x^((3)/(2)). This means we are looking for an expression that represents the square root of x cubed, multiplied by 2.Analyze first option: Analyze the first option. The first option is sqrt(2x^(3)). This represents the square root of the product of 2 and x cubed. This is not the same as 2 times the square root of x cubed because the 2 is inside the square root.Analyze second option: Analyze the second option. The second option is root(3)(2x^(2)). This represents the cube root of the product of 2 and x squared. This is not equivalent to the given expression because the given expression has a square root, not a cube root, and the exponent of x is different.Analyze third option: Analyze the third option. The third option is 2root(3)(x^(2)). This represents 2 times the cube root of x squared. Again, this is not equivalent to the given expression because the given expression has a square root, not a cube root.Analyze fourth option: Analyze the fourth option. The fourth option is 2sqrt(x^(3)). This represents 2 times the square root of x cubed, which is the same as 2 times x raised to the power of (3/2). This matches the given expression 2x^((3)/(2)).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Select the expression that is equivalent to
2x^((3)/(2))

sqrt(2x^(3))

root(3)(2x^(2))

2root(3)(x^(2))

2sqrt(x^(3))

Select the expression that is equivalent to $2 x^{\frac{3}{2}}$ $\newline$ $\sqrt{2 x^{3}}$ $\newline$ $\sqrt[3]{2 x^{2}}$ $\newline$ $2 \sqrt[3]{x^{2}}$ $\newline$ $2 \sqrt{x^{3}}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

2 x^{\frac{3}{2}}

\newline

\sqrt{2 x^{3}}

\newline

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

\newline

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

\newline

2 \sqrt{x^{3}}

Understand given expression: Understand the given expression. $\newline$ The given expression is $2x^{\left(\frac{3}{2}\right)}$ . This means we are looking for an expression that represents the square root of $x$ cubed, multiplied by $2$ .
Analyze first option: Analyze the first option. $\newline$ The first option is $\sqrt{2x^{3}}$ . This represents the square root of the product of $2$ and $x$ cubed. This is not the same as $2$ times the square root of $x$ cubed because the $2$ is inside the square root.
Analyze second option: Analyze the second option. $\newline$ The second option is $\sqrt[3]{2x^{2}}$ . This represents the cube root of the product of $2$ and $x$ squared. This is not equivalent to the given expression because the given expression has a square root, not a cube root, and the exponent of $x$ is different.
Analyze third option: Analyze the third option. $\newline$ The third option is $2\sqrt[3]{x^{2}}$ . This represents $2$ times the cube root of $x$ squared. Again, this is not equivalent to the given expression because the given expression has a square root, not a cube root.
Analyze fourth option: Analyze the fourth option. $\newline$ The fourth option is $2\sqrt{x^{3}}$ . This represents $2$ times the square root of $x$ cubed, which is the same as $2$ times $x$ raised to the power of $(3/2)$ . This matches the given expression $2x^{\left(\frac{3}{2}\right)}$ .