➕ Algebra 1 · Exponents and Polynomials

Zero and Negative Exponents practice questions

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Answer key with explanations

1. Evaluate 7⁻².

   Answer: 1/49. A negative exponent means the reciprocal of the positive power: 7⁻² = 1/7² = 1/49. The answer −49 wrongly makes the number negative, −14 multiplies 7 by −2, and 1/14 multiplies 7 by 2 on the bottom.

2. Simplify (13y)⁰, with y ≠ 0.

   Answer: 1. Any nonzero base to the power 0 is 1. The parentheses put the whole 13y inside the base, so (13y)⁰ = 1. Without the parentheses, 13y⁰ would equal 13.

3. Write 8x⁻² with only positive exponents (x ≠ 0).

   Answer: 8/x². Only x has the exponent −2, so only x moves to the denominator: 8x⁻² = 8 · (1/x²) = 8/x². The 8 stays on top. The choice 1/(64x²) would be the answer for (8x)⁻².

4. Evaluate (3/5)⁻².

   Answer: 25/9. Flip the fraction and make the exponent positive: (3/5)⁻² = (5/3)² = 25/9. Not flipping gives 9/25. The answer is positive, because a negative exponent does not make a number negative.

5. Simplify x⁻² · x⁷ (assume x ≠ 0).

   Answer: x⁵. Same base, product rule: add the exponents, −2 + 7 = 5, so the answer is x⁵. Multiplying the exponents (−2 · 7 = −14) is the power-of-a-power rule, not this one. The choice x⁹ ignores the minus sign, and x⁻⁵ comes from computing 2 − 7 instead of −2 + 7.

6. Simplify x³ ÷ x⁸ and write the answer with a positive exponent (x ≠ 0).

   Answer: 1/x⁵. Subtract the exponents: 3 − 8 = −5, so x³ ÷ x⁸ = x⁻⁵ = 1/x⁵. Subtracting the other way (8 − 3) gives x⁵, which is wrong. Try x = 2: 2³ ÷ 2⁸ = 8/256 = 1/32, not 32.

7. Simplify (x⁻²y³)⁻² and write the answer with positive exponents (assume x ≠ 0 and y ≠ 0).

   Answer: x⁴/y⁶. Apply the exponent −2 to each factor and multiply the exponents: (x⁻²)⁻² = x⁴ and (y³)⁻² = y⁻⁶. That gives x⁴y⁻⁶. Move y⁻⁶ to the bottom: x⁴/y⁶.

8. Ravi wrote 11⁻² = −22. Which statement correctly describes his mistake and the right value?

   Answer: He multiplied 11 by −2. The correct value is 1/11² = 1/121.. A negative exponent means a reciprocal, not “times a negative number.” 11⁻² = 1/11² = 1/121. Ravi’s −22 comes from computing 11 · (−2).

9. A gram is 10⁻³ kilograms. How many kilograms is 250 grams?

   Answer: 0.25 kilograms. 250 × 10⁻³ = 250 × (1/1000) = 250/1000 = 0.25 kilograms. A negative exponent makes the number smaller here: you divide by 1000, you do not multiply.