The repeated-factor print shop

The press shortens multiplication without changing its value.

Power Press

Expanded form · intake

x·x·x

→

Exponent form · proof

x³

BASE = xThe factor that repeats.

EXPONENT = 3How many matching factors.

COUNT IDENTICAL FACTORS

three 4s → 4³andfour cs → c⁴

4³c⁴expands to4·4·4·c·c·c·c

Only repeated factors get exponents

A factor that appears once stays exactly as it is.

single

3

LEAVE 3

t lane

tttt

COUNT 4

COUNT ONLY THE REPEATED t

3 · (t · t · t · t) = 3t⁴

Do not write 3⁴. The 3 appears only once.

A whole bracket can be the base

Keep a repeated group together before you count it.

single

9

LEAVE 9

group lane

(p + 1)(p + 1)

COUNT 2

BASE = THE WHOLE GROUP (p + 1)

9 · (p + 1) · (p + 1) = 9(p + 1)²

(p + 1)²means two matching bracket factors

Your turn at the press

Sort the 3s and xs into separate factor lanes.

3 · 3 · x · x · x · x

3

·

x

count the 3s

count the xs

Stamp my exponents

One exponent for each repeated factor.

Work on your whiteboardWrite 3 · 3 · x · x · x · x using exponents.Submitted — your proof sheet is ready.

Sort, count, stamp

Each lane creates one base-and-exponent pair.

3 lane

33

COUNT 2

x lane

xxxx

COUNT 4

TWO 3s · FOUR xs

3 · 3 · x · x · x · x = 3²x⁴

3²x⁴expands back to six factors in two lanes

3²x⁴

bⁿ

Power Press certified.

Exponent notation is a shorter label for repeated multiplication.

1 · SpotFind factors that repeat.

2 · SortPut identical factors together.

3 · CountCount each factor lane.

4 · StampBase = factor.
Exponent = count.