EXPONENTS 2 X X TO THE SECOND POWER
- Slides: 27
EXPONENTS
2 X 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
3 X 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
4 X X TO THE FOURTH POWER X IS CALLED BASE 4 IS CALLED EXPONENT Use x as a factor 4 times X*X*X*X
2 3 3 TO THE SECOND POWER OR 3 SQUARED Use 3 as a factor 2 times 3*3 2 = 3 9
3 3 3 TO THE THIRD POWER OR 3 CUBED Use 3 as a factor 2 times 3*3*3 3 = 3 27
POWERS OF BASE 10 101 102 103 104 105 106 = = = = 1 10 1000 10, 000 100, 000 1, 000
POWERS OF BASE 2 20 21 22 23 24 25 26 = = = = 1 2 4 8 16 32 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 x 2 x 2 x 2
POWERS OF BASE 3 30 31 32 33 34 35 36 = = = = 1 3 9 27 81 243 729 Any base to the zero power equals 1 Any base to the one power equals itself 3 x 3 3 x 3 x 3 x 3 x 3 x 3
TRY IT OUT 100 = 1 50 = 1 23 = 8 34 = 81 53 = 125 25 = 32
TRY IT OUT 103 = 160 1000 = 1 62 = 36 52 = 25 43 = 64 73 = 343
MULTIPLYING EXPONENTS WITH THE SAME BASE
2 X * 3 X = 5 X X * X * X* X Keep the base ADD the Exponents
() () PARENTHESES mean TIMES 2 (10 ) 3 (10 ) = 5 10 10 * 10 Keep the base ADD the Exponents
() () PARENTHESES mean TIMES 3 (Y 2 X) 4 (Y 3 X) = 7 5 YX (Y * Y * X) * (Y * Y* Y * X * X) Keep the base ADD the Exponents
TRY IT OUT 5 * 5 2 * 53 = 56 Don’t forget the one exponent is implied X*Y * 2 3 X *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 2 (X 2 Y 3 Z ) 4 (Y 5 = Z) X 2 Y 6 Z 8 Don’t forget the one exponent is implied
DIVIDING EXPONENTS WITH THE SAME BASE
5 X Keep the base / 3 X = 2 X SUBTRACT the Exponents
6 10 Keep the base / 2 10 = 4 10 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 10 -3 = 1 103 OR 1 1000 OR 0. 001
Examples 2 -3 = 1 23 OR 1 8 OR 0. 125
Examples 2 -3 = 1 23 Negative Exponent To Reciprocal To Fraction To Decimal OR 1 8 OR 0. 125
MORE EXAMPLES 10 – 1 = 101 10 – 2 = 1 102 1 = 0. 1 10 = 1 100 = 0. 01
MORE EXAMPLES 10 – 3 = 103 10 – 4 = 1 104 1 = 0. 001 1000 = 1 10000 = 0. 0001
MORE EXAMPLES 10 – 5 = 105 10 – 6 = 1 106 = 1 = 0. 00001 100, 000 1 = 1, 000 0. 000001