The Rules of Exponents

One page. Three moves — everything else is an echo.

ADD · SUBTRACT · MULTIPLY
multiplying · dividing · a power of a power — the only three moves there are
Product RuleADD

xm · xn = xm+n

23 · 22 = 25 = 32

Same base, multiplying: add the exponents.

Quotient RuleSUBTRACT

xm ÷ xn = xm−n

25 ÷ 22 = 23 = 8

Same base, dividing: subtract the exponents.

Power of a PowerMULTIPLY

(xm)n = xmn

(22)3 = 26 = 64

A power raised to a power: multiply the exponents.

Power of a ProductDISTRIBUTE

(xy)n = xnyn

(2 · 3)2 = 22 · 32 = 36

One exponent outside: everyone inside gets a copy.

Power of a QuotientDISTRIBUTE

(x/y)n = xn/yn

(2/3)2 = 22/32 = 4/9

Top and bottom each get a copy of the exponent.

Zero ExponentONE

x0 = 1 (x ≠ 0)

70 = 1

Because x3/x3 is both 1 and x0 — so they're equal.

Negative ExponentFLIP

x−n = 1/xn

2−3 = 1/23 = 1/8

Cross the fraction bar, flip the sign.

Fractional ExponentROOT

xm/n = (n√x)m

43/2 = (√4)3 = 23 = 8

Bottom = the root, top = the power. Root first.

x3 · y2 Different bases? Nothing combines, nothing to distribute — leave it be. Every rule above needs either one shared base or one exponent outside a parenthesis.

One page. Prints clean black on white, easy on the ink — the dark background stays on the screen.