Digital PSAT Math Practice Question 300: Answer and Explanation

Question: 300

Given that x > 0, which of the following is an equivalent form of

• A. 4x
• B. 16x²
• C.
• D.

Correct Answer: A

Explanation:

(A) Looking at the four answer choices, you can see that you should simplify your original expression in some way so that there are no longer any square roots. First try to simplify the expression in the parenthesis, . This tells you to raise every factor inside the parentheses to the power. In other words, you have . Now, since the 3 in the denominator of tells us to take the cube root of 64 (resulting in 4) and the 2 in the numerator tells us to square the result (giving us 4² = 16). Also, . Thus, you can rewrite the expression in parentheses as

Now, step back and look at the entire expression inside the square root, , which is equivalent to 16x⁴ x^-2 by your above work. Since x⁴ x^-2 = x^4-2 = x², your expression becomes 16x².

Thus, the original expression given in the statement of the problem, , can be rewritten as Since which matches choice (A).