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Fractions practice

Powers of fractions

Evaluate exact powers of fractional bases, with selected integer or rational exponents and explicit attention to signs and reciprocals.

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Worksheet · LetterWorksheet · A4
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Read the parentheses around the base and identify the exponent type. Apply the appropriate power, reciprocal or root operation to the full fraction, then simplify exactly. Fractional-exponent practice uses values constructed to have valid exact rational results.

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A4

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Learning objective

What this activity builds

Apply exponent laws to the entire fractional base while distinguishing a negative base, a negative exponent and a fractional exponent.

Worked example

Evaluate (-2/3) raised to the power -2.

9/4.

The negative exponent takes a reciprocal: (-2/3)^(-2) = (-3/2)^2. Squaring multiplies the negative fraction by itself, giving the positive value 9/4.

Teaching notes

Make the practice count

  • Separate the sign of the base from the sign of the exponent when reading aloud.
  • Review zero and negative powers only with nonzero bases.
  • This is advanced algebra readiness, not a blanket Grade 6 skill. For negative bases with rational powers, the reduced root degree must be odd for the real-valued constructions used here.

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Bases
Exponents
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Math SheetNameScoreTeacherDate/ 20Fraction ExponentsEvaluate exact powers with the selected base and exponent types.1.682=2.-66-8=3.-523=4.56-3=5.-745=6.68-5=7.-647=8.-75-6=9.-886=10.66-2=11.525=12.47-7=13.887=14.68-3=math-sheet.comPage 1 / 2
Math SheetNameScoreTeacherDate/ 20Fraction ExponentsEvaluate exact powers with the selected base and exponent types.15.647=16.38-5=17.-773=18.67-6=19.322=20.78-6=math-sheet.comPage 2 / 2

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