Describe how to transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a rational exponent. Make sure you respond with complete sentences.

Question

jhonyy9 · Answer

$$\left( \sqrt[3]{x^{4}} \right)^{5} = ?$$

Renne · Answer

To transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a rational exponent, we can use the exponent rules. First, we can raise the third root of x to the fourth power by multiplying the exponent of 1/3 by 4, which gives us x^(4/3). Then, we can raise x^(4/3) to the fifth power by multiplying the exponent of 4/3 by 5, which gives us x^(20/3). Therefore, the expression with a rational exponent that is equivalent to the quantity of the third root of x to the fourth power, to the fifth power is x^(20/3).

jhonyy9 · Answer

@renne wrote:

To transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a rational exponent, we can use the exponent rules. First, we can raise the third root of x to the fourth power by multiplying the exponent of 1/3 by 4, which gives us x^(4/3). Then, we can raise x^(4/3) to the fifth power by multiplying the exponent of 4/3 by 5, which gives us x^(20/3). Therefore, the expression with a rational exponent that is equivalent to the quantity of the third root of x to the fourth power, to the fifth power is x^(20/3).

explained perfect

Renne · Answer

@jhonyy9 wrote:

@renne wrote:

To transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a rational exponent, we can use the exponent rules. First, we can raise the third root of x to the fourth power by multiplying the exponent of 1/3 by 4, which gives us x^(4/3). Then, we can raise x^(4/3) to the fifth power by multiplying the exponent of 4/3 by 5, which gives us x^(20/3). Therefore, the expression with a rational exponent that is equivalent to the quantity of the third root of x to the fourth power, to the fifth power is x^(20/3).

explained perfect

Thank you.