Apply the rules for multiplying, dividing, and raising powers — including the ones that trip up strong students: zero, negative, and fractional exponents. Every question comes with a written explanation of which rule applies and why.
x³·y² isn't x⁵ — the product rule only works when the base is the same on both sides of the multiplication.
x⁻² means 1/x², not −x². The sign controls where the term sits — numerator or denominator — not the value itself.
(x³)² is x⁶, not x⁵ — exponents multiply under a power of a power, but add when you're multiplying two terms with the same base. Mixing the two rules up is the most common error in this subtopic.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Simplify: x⁵ · x³
A — x⁸. When multiplying powers with the same base, add the exponents: 5 + 3 = 8, giving x⁸. x¹⁵ (B) comes from multiplying the exponents instead of adding them — the power-of-a-power rule applied to the wrong situation.
Simplify: x⁻³ · x⁷
A — x⁴. Even with a negative exponent, the product rule still applies: add the exponents, −3 + 7 = 4, giving x⁴. x⁻⁴ (B) comes from subtracting instead of adding — treating the negative sign as an instruction to subtract rather than as part of the exponent's value. 1/x⁴ (D) is the same wrong answer written as a fraction.
Simplify: (8x⁶)^(2/3)
A — 4x⁴. Apply the fractional exponent to each factor separately: 8^(2/3) means squaring the cube root of 8, which is 2² = 4, and x⁶ raised to 2/3 gives x^(6·2/3) = x⁴. Multiplying those together gives 4x⁴. 4x⁹ (B) comes from adding 6 and 2/3 as if the product rule applied, instead of multiplying under the power-of-a-power rule. 64x⁴ (C) comes from squaring 8 fully (8² = 64) instead of taking the cube root first.
Exponent rules are short, but the exam mixes several in one expression — practice is about recognizing which rule applies to which piece.
For each step, say which rule you're using — product, quotient, power, or root — before writing anything. Untimed practice is where that labeling habit sticks.
Move to timed sessions once rule selection is automatic. Exponent problems are quick once you're not second-guessing which rule fits.
Pair exponents with radicals and scientific notation in a mock — all three share the same underlying rules, just dressed differently.
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