Bluebook SAT Test SAT Exponents and Radicals Practice 5

Question 1

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

Accepted Answer

1.08 × 10⁵

Answer

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

Question 2

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

Accepted Answer

x²y

Answer

⁴√(x⁸y⁴) = x^(8/4) × y^(4/4) = x²y.

Question 3

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

Accepted Answer

8

Answer

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

Question 4

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

Accepted Answer

8 + 4√3

Answer

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

Question 5

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

Accepted Answer

x = 3/4

Answer

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

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