EXPONENTS

X2X2 X TO THE SECOND POWER OR X SQUARED X IS CALLED BASE 2 IS CALLED EXPONENT Use x as a factor 2 times X * X

X3X3 X TO THE THIRD POWER OR X CUBED X IS CALLED BASE 3 IS CALLED EXPONENT Use x as a factor 3 times X * X *X

X4X4 X TO THE FOURTH POWER X IS CALLED BASE 4 IS CALLED EXPONENT Use x as a factor 4 times X * X * X * X

TO THE SECOND POWER OR 3 SQUARED Use 3 as a factor 2 times 3 * = 9

3 3 TO THE THIRD POWER OR 3 CUBED Use 3 as a factor 2 times 3 * 3 * = 27

POWERS OF BASE = = = = = 10, = 100, = 1,000,000

POWERS OF BASE = = = = = = = 64 Any base to the zero power equals 1 Any base to the one power equals itself 2 x 2 2 x 2 x 2 2 x 2 x 2 x 2 2 x 2 x 2 x 2 x 2 2 x 2 x 2 x 2 x 2 x 2

POWERS OF BASE = = = = = = = 729 Any base to the zero power equals 1 Any base to the one power equals itself 3 x 3 3 x 3 x 3 3 x 3 x 3 x 3 3 x 3 x 3 x 3 x 3 3 x 3 x 3 x 3 x 3 x 3

TRY IT OUT 10 0 = = = = = = 32

TRY IT OUT 10 3 = 16 0 = = = = =

MULTIPLYING EXPONENTS WITH THE SAME BASE

X 2 * X 3 = X 5 X * X * X * X* X Keep the base ADD the Exponents

(10 2 ) (10 3 ) = * 10 * 10 * 10* 10 Keep the base ADD the Exponents () () PARENTHESES mean TIMES

(Y 3 X 2 ) (Y 4 X 3 ) = Y 7 X 5 ( Y * Y * Y * X * X) * (Y * Y* Y * Y * X * X * X) Keep the base ADD the Exponents () () PARENTHESES mean TIMES

TRY IT OUT 5 * 5 2 * 5 3 = 5 6 Don’t forget the one exponent is implied X * Y 2 * X 3 * Y = X 4 Y 3 Don’t forget the one exponent is implied

TRY IT OUT (XY 3 ) ( X 2 Y 3 ) = X 3 Y 6 Don’t forget the one exponent is implied (X 2 Y 2 Z 3 ) (Y 4 Z 5 ) = X 2 Y 6 Z 8 Don’t forget the one exponent is implied

DIVIDING EXPONENTS WITH THE SAME BASE

X 5 / X 3 = X 2 Keep the base SUBTRACT the Exponents

10 6 / 10 2 = 10 4 Keep the base SUBTRACT the Exponents

Negative Exponents Negative exponents are NOT negative numbers Negative exponents are fractions or decimals Negative exponents are greater than 0 but less than one

Examples = OR OR 0.001

Examples 2 -3 = OR 1 8 OR 0.125

Examples 2 -3 = OR 1 8 OR Negative Exponent To Reciprocal To Fraction To Decimal

MORE EXAMPLES 10 –1 = 1 = 1 = –2 = 1 = 1 =

MORE EXAMPLES 10 –3 = 1 = 1 = –4 = 1 = 1 =

MORE EXAMPLES 10 –5 = 1 = 1 = , –6 = 1 = 1 = ,000,000