Exponent Rules Flashcards

Grade 8 · Math · Flashcards

All the laws of exponents — memorize and master.

Flashcards

Product rule: x^m * x^n = x^(m+n). Add exponents, same base.
Quotient rule: x^m / x^n = x^(m-n). Subtract exponents, same base.
Power rule: (x^m)^n = x^(m*n). Multiply the exponents.
Power of a product: (xy)^n = x^n * y^n. Exponent applies to each factor.
Power of a quotient: (x/y)^n = x^n / y^n.
Zero exponent: x^0 = 1 for x not equal to 0.
Negative exponent: x^(-n) = 1/x^n. Flip to denominator, make positive.
x^(-1): = 1/x — the reciprocal.
Simplifying (2x^3)^4: 2^4 * x^(3*4) = 16x^12. Apply power rule to coefficient AND variable.
Same base required: Product/quotient rules only apply to identical bases. x^3 * y^2 cannot be combined.
Negative base, even exponent: (-2)^4 = +16 — result is positive.
Negative base, odd exponent: (-2)^3 = -8 — result is negative.