Question

Rewrite in simplest rational exponent form square root x times 4 square root x

Answer 1

To rewrite the expression in simplest rational exponent form, we express the square roots as the variable x raised to the power of 0.5, then multiply and simplify the exponents, resulting in 4x.

Step-by-step explanation:

The student asked to rewrite the expression square root of x times 4 square root of x in simplest rational exponent form. To do this, we apply the rules for exponents and roots to express the given expression in a simpler form. The square root of any variable, x, can be expressed as x raised to the power of 0.5, which means square root of x is x0.5. The expression 4 square root of x can be rewritten as 4x0.5. When we multiply x0.5 with 4x0.5, we apply the rule of multiplying powers with the same base: we add the exponents together.

This yields x0.5 × 4x0.5 = 4x1, since 0.5 + 0.5 equals 1. Therefore, the expression in simplest rational exponent form is 4x.

Answer 2

`√(x) *4 √(x)` is what I think you're saying. Converting this to exponential form, the square root becomes a 1/2. So the square root of x is rewritten as x^(1/2). Same with the 4 times the square root of x. That can be rewritten as 4x^(1/2). The rule about multiplying exponents when the bases are the same is to add the exponents, right. So x^(1/2)*4x^(1/2) = 4x^1 or 4x