Question

The first two steps that a student uses to rewrite the expression sqrt[3](5)· 125^(frac 1)2 are shown below. sqrt[3](5)· 125^(frac 1)2 Step1:5^(frac 1)3· 125^(frac 1)2 Step2:5^(frac 1)3· (5^3)^ 1/2 What operation should the student complete after Step 2? A Add the exponents 3 and 1/2 . B Add the exponents 1/3 and 3. C Multiply the exponents 1/3 and 3. D Multiply the exponents 3 and

Answer 1

1/2.

The correct answer is D - Multiply the exponents 3 and 1/2.

In Step 2, the student rewrote 125 as (5^3) because 125 is equal to 5 raised to the power of 3.

To simplify the expression further, the student can now multiply the exponents 3 and 1/2.

Since 3 is already in fractions and 1/2 can be written as 3/6, the student can multiply the exponents to get 3 * 3/6 = 9/6 = 3/2.

Therefore, the final expression is 5^(1/3) * (5^3)^(1/2) = 5^(1/3) * 5^(3/2).