Exponent Rules
Question
Answer choices
- x^6
- x^5
- x^6
- x^7
- x^2
A Correct answer: A) x^6
Set up the problem carefully before computing. Power of a power: multiply exponents. Product of powers with same base: add exponents. Quotient of powers with same base: subtract exponents.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
(x^2)^2 = x^4 by the power-of-a-power rule. Then x^4 · x^2 = x^6 by the product rule. Final answer: x^6.
Why each wrong answer is wrong
- B) x^5: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) x^6: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) x^7: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) x^2: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Memorize the three exponent rules: x^a · x^b = x^(a+b); x^a / x^b = x^(a-b); (x^a)^b = x^(ab). The ACT tests these constantly.
More Hard Intermediate Algebra
- Solving a Quadratic by FactoringSolve for x: x^2 - 3 x + 2 = 0.
- Function EvaluationIf f(x) = 3x^2 - 2, what is f(3)?
- System of Linear EquationsSolve the system: 1x + 1y = 4 and x + y = 4. Express your answer as (x, y).
- Solving a Quadratic by FactoringSolve for x: x^2 - 4 x + 3 = 0.
- Function EvaluationIf f(x) = 3x^2 - 1, what is f(3)?