Algebra 1 Practice Test: Exponent Rules

When you multiply powers with the same base, add the exponents: 3 + 5 = 8. Multiplying the exponents gives the trap x¹⁵.

A power of a power multiplies the exponents: 4 · 3 = 12. Adding them gives x⁷.

Dividing powers with the same base subtracts the exponents: 10 − 4 = 6. Dividing the exponents gives x^2.5.

Raise each factor to the 4th power: 2⁴ = 16 and (x³)⁴ = x¹². Leaving the 2 unchanged gives 2x¹².

Any nonzero number to the zero power is 1, so 3x⁰ = 3 · 1 = 3 and 2⁰ = 1. The exponent 0 applies only to x, not to the 3.

A negative exponent means a reciprocal: 2⁻³ = 12³ = 18. It does not make the result negative.

Subtract exponents: x^{−2 − 4} = x⁻⁶ and y^{3 − (−1)} = y⁴. So the result is y⁴x⁶. Treating −(−1) as −1 gives y².

Multiply the coefficients: 3 · (−4) = −12. Add exponents on like bases: a^{2 + 3} = a⁵ and b^{1 + 5} = b⁶. Adding 3 and −4 gives the trap −1.

Add the exponents: 3 + (−5) = −2, so 4⁻² = 116. Ignoring the negative sign gives 16.

Multiply the numbers: 3 · 2 = 6, and add the exponents of 10: 4 + 5 = 9. Multiplying the exponents gives 10²⁰.