Question

Write 5 times x to the two thirds power in radical form. 5 times the square root of x to the third power the square root of quantity 5 times x to the third power 5 times the cube root of x to the second power the cube root of quantity 5 times x to the second power

Answer 1

To express '5 times x to the two thirds power' in radical form, it translates to '5 times the cube root of x squared'.

Step-by-step explanation:

To write 5 times x to the two thirds power in radical form, you can follow the rules of exponents and radicals. The expression 5 times x to the two thirds power can be written as 5 × x2/3, which in radical form becomes 5 × the cube root of x squared. The fractional exponent indicates that we are taking the cube root (since the denominator is 3), and then squaring the result (since the numerator is 2).

Answer 2

To express 5 times x to the two-thirds power in radical form, it is written as 5 times the cube root of x squared.

Step-by-step explanation:

The question is asking to express 5 times x to the two-thirds power in radical form. In mathematics, we can convert fractional exponents into radical notation because they represent roots. Specifically, an exponent of 1/2 represents a square root, while an exponent of 1/3 represents a cube root. Now, to write the expression 5x2/3 in radical form, you break apart the exponent into its two components: the cube root and the squaring operation. We apply the cube root first followed by the squaring operation because the denominator of the fraction indicates the root. Therefore, our expression in radical form is:

5 times the cube root of x squared, or mathematically:

5√(x2)