Grade 8 Math Practice Test: Properties of Integer Exponents

Same base, so add the exponents: 3 + 4 = 7. 5¹² multiplies the exponents, which is the rule for a power of a power.

Any nonzero number to the zero power is 1. For example 7² ÷ 7² = 7⁰, and any number divided by itself is 1.

A negative exponent means the reciprocal: 2⁻³ = 1 ÷ 2³ = 1/8. It does not make the number negative, so −8 is wrong.

For a power of a power, multiply the exponents: 2 × 3 = 6. 4⁵ adds the exponents, which is the rule for multiplying powers.

Subtract the exponents: 5 − 7 = −2, and 6⁻² = 1/36. 36 subtracts in the wrong order (7 − 5).

(3⁻²)² = 3⁻⁴, and 3⁻⁴ × 3⁵ = 3¹ = 3. 27 ignores the outer exponent 2 and works out 3⁻² × 3⁵ = 3³.

125 = 5³, so 1/125 = 5⁻³. −5³ equals −125, a negative number, not a fraction.

A power of a product is the product of the powers: (2 × 5)⁴ = 2⁴ × 5⁴ = 16 × 625 = 10,000. 2 × 5⁴ raises only the 5 to the fourth power.

(−2)⁴ = (−2)(−2)(−2)(−2) = 16, because an even number of negative factors gives a positive product. −16 is the value of −2⁴ without parentheses.

Numerator: 3 + (−5) = −2. Dividing: −2 − (−4) = 2, so the result is 10² = 100. 10⁻⁶ subtracts 4 instead of subtracting −4.