SAT Exponents and Radicals Practice Flashcards

What is (5.4 × 10⁶) × (2.0 × 10⁻²) in scientific notation?

Answer: 1.08 × 10⁵

5.4 × 2.0 = 10.8; exponent = 6 + (−2) = 4. So 10.8 × 10⁴ = 1.08 × 10⁵.

Which of the following is equivalent to ⁴√(x⁸y⁴)?

Answer: x²y

⁴√(x⁸y⁴) = x^(8/4) × y^(4/4) = x²y.

If 5^a × 5^b = 5^12 and a − b = 4, what is the value of a?

Answer: 8

a + b = 12 and a − b = 4. Adding: 2a = 16, a = 8.

Rationalize the denominator of 4/(2 − √3).

Answer: 8 + 4√3

Multiply by (2+√3)/(2+√3): 4(2+√3)/(4−3) = 4(2+√3) = 8 + 4√3.

Solve for x: 9^(2x) = 27

Answer: x = 3/4

9^(2x) = 3^(4x) and 27 = 3³. So 4x = 3, x = 3/4.

What is the simplified form of √45 ÷ √5?

Answer: 3

√45 ÷ √5 = √(45/5) = √9 = 3.

An investment grows as A = 1000 × (1.06)^t. Using log 2 ≈ 0.301 and log 1.06 ≈ 0.0253, in how many years does it approximately double?

Answer: 12

1.06^t = 2 → t = log2/log1.06 ≈ 0.301/0.0253 ≈ 11.9 ≈ 12 years.