(NTR) Negatives in Arithmetic and Exponents

Vocabulary flashcards covering how negative numbers behave in addition, multiplication/division, chaining, and exponent rules with and without parentheses.

Negative plus negative

Sum of two negative numbers is negative; e.g., -4 + -11 = -15.

Product of negatives

Product of two negative numbers is positive; e.g., (-5) × (-3) = 15.

Quotient of negatives

Quotient of two negative numbers is positive; e.g., -10 ÷ -2 = 5.

Sign pattern with negative factors

An even number of negative factors yields a positive product; an odd number yields a negative product. Example: (-5) × (-3) × (-2) = -30.

(-a)^2

A negative number inside parentheses squared gives a positive result. Example: (-4)^2 = 16.

-a^2

Without parentheses, the negative sign is outside the square, so the result is negative. Example: -4^2 = -16.

(-a)^n with even n

If a is negative and you raise to an even exponent with parentheses around the base, the result is positive. Example: (-4)^4 = 256.

(-a)^n with odd n

If the exponent is odd with the base in parentheses, the result is negative. Example: (-3)^3 = -27.

Unparenthesized negative base to a power

Without parentheses, a negative base to a positive exponent n equals -(a^n); the negative sign remains outside the power. Example: -5^3 = -125.