Powers of Rational Numbers
A power is repeated multiplication of the same factor; a negative base is positive for even exponents, negative for odd
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A power is repeated multiplication of the same factor; a negative base is positive for even exponents, negative for odd
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A power is compact repeated multiplication: aⁿ means n copies of a multiplied together. With a negative base the signs follow a pattern — negative factors pair up to give positive, so even exponents end positive; an odd exponent leaves one negative factor unpaired, so the result is negative. Play with the base and exponent and watch the expansion and pairing make the rule obvious.
A power is repeated multiplication: (−2)³ = (−2)×(−2)×(−2). Adjust the base and exponent with buttons and watch the factors pop in and pair up, revealing the sign rule for negative bases — even exponents give positive, odd exponents give negative. Random bases and exponents for endless practice.