Apply exponent rules and evaluate integer powers.
Free, timed SHSAT practice sets on exponents & powers— every question includes a full worked explanation, and there's no account required.
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An exponent tells you how many times to multiply the base by itself: \(3^4 = 3 \times 3 \times 3 \times 3 = 81\), not \(3 \times 4 = 12\).
Negative bases: an even exponent gives a positive answer and an odd exponent gives a negative one. \((-2)^4 = 16\) and \((-2)^3 = -8\). Without parentheses, \(-2^4 = -16\), because the exponent applies only to the 2.
Rules for the same base:
Use the rule first, then work out the power. This keeps the numbers small.
Common traps: multiplying the base by the exponent, and mixing up the rules (adding when you must multiply).
\((-7)^{4}\) means (-7) multiplied by itself 4 times: \((-7)^{4} = 2401\). Multiplying the base by the exponent gives \(-28\). Getting the sign of the answer wrong gives \(-2401\). Using the base as a factor only 3 times gives \(-343\).
With the same base, subtract the exponents: \(8^{5} \div 8^{2} = 8^{3} = 512\). Subtracting the two powers instead of dividing them gives \(32704\). Dividing the bases too (as \(1^{3}\)) gives \(1\). Subtracting the exponents and then multiplying 8 by 3 gives \(24\).
With the same base, multiply the exponents: \((3^{2})^{4} = 3^{8} = 6561\). Adding the exponents instead of multiplying them gives \(729\). Multiplying \(3^{2}\) by 4 instead of raising it to the power 4 gives \(36\). Multiplying 3 by both exponents gives \(24\).