Math Exponents, Radicals, and Scientific Notation

Question 1

Simplify: (3²)³

Accepted Answer

729

Answer

(3²)³ = 3^(2×3) = 3⁶ = 729. When raising a power to a power, multiply the exponents.

Question 2

Which of the following equals 4.5 × 10⁻³?

Accepted Answer

0.0045

Answer

A negative exponent moves the decimal left. 4.5 × 10⁻³ = 4.5 ÷ 1000 = 0.0045.

Question 3

Simplify: √72

Accepted Answer

6√2

Answer

72 = 36 × 2 → √72 = √36 × √2 = 6√2.

Question 4

What is the value of 27^(2/3)?

Accepted Answer

9

Answer

27^(2/3) = (27^(1/3))² = 3² = 9. The denominator of the fractional exponent is the root, and the numerator is the power.

Question 5

Which expression is equivalent to x⁻⁴?

Accepted Answer

1/x⁴

Answer

A negative exponent means the reciprocal: x⁻ⁿ = 1/xⁿ. So x⁻⁴ = 1/x⁴.

Math Practice Test