Bluebook SAT Test SAT Exponents and Radicals Practice 8

Question 1

Which of the following equals (a⁴ × b⁶)^(1/2)?

Accepted Answer

a²b³

Answer

(a⁴b⁶)^(1/2) = a^(4/2) × b^(6/2) = a²b³.

Question 2

An exponential function is y = 3 × 2^x. What is the percent increase from x = 2 to x = 3?

Accepted Answer

100%

Answer

At x=2: y=12; at x=3: y=24. Percent increase = (24−12)/12 × 100 = 100%.

Question 3

What is the value of 4^(3/2) + 8^(2/3)?

Accepted Answer

12

Answer

4^(3/2) = (√4)³ = 8 and 8^(2/3) = (∛8)² = 4. Sum = 8 + 4 = 12.

Question 4

Simplify: (3^n × 9^n) / 27^n

Accepted Answer

1

Answer

9^n = 3^(2n) and 27^n = 3^(3n). Numerator = 3^n × 3^(2n) = 3^(3n). Ratio = 3^(3n)/3^(3n) = 1.

Question 5

Solve: √(2x − 3) = √(x + 7)

Accepted Answer

x = 10

Answer

Square both sides: 2x − 3 = x + 7 → x = 10. Verify: √17 = √17 ✓.

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