EXPONENTS

Multiplication is repeated addition: 3 x 4 = 3 + 3 + 3 + 3 Exponents or powers are repeated multiplication: 34 = 3 x 3 x 3 x 3

Squaring a Number: Taking a number to the second power Example: "3 squared" means 3 to the second power: 32 = 9 Cubing a Number: Taking a number to the third power Example: "4 cubed" means 4 to the third power: 43 = 64

Negative Numbers and Powers: i.) -32 = -9 Operations: Exponent and subtraction (represented by negative sign). Because exponents come first, 3 is squared, then made negative.

ii.) (-3)2 = 9 Operations: Exponent. The number -3 is squared (multiplied by itself): (-3)(-3) = 9

Example: Find x2 for x = -5

This is Case (ii): (-5)2 = 25. If done like Case (i), the value of 5 would be squared, NOT -5. But we were asked to square x, which is -5, so we must multiply -5 by itself as in Case (ii).

Powers of Zero and One: a0 = 1 a1 = a

SCIENTIFIC NOTATION

Converting from Scientific Notation to Standard Notation: 1.) The exponent tells you how many places to move the decimal point.

If the exponent is positive, the number is "large" (greater than one) so move the decimal point that many places right. If it is negative, the number is "small" (between zero and one) so move the decimal point left.

Add zeroes if necessary.

Converting from Standard Notation to Scientific Notation: 1.) There must be one significant digit to the left of the decimal point. Count how many places you will need to move the decimal point so that this occurs. This is the exponent.

If the number is "large" (greater than one), the exponent is positive. If the number is "small" (between zero and one), the exponent is negative.

2.) Write the number with one significant digit in front of the decimal point, remove all unnecessary zeroes, and multiply by a power of ten with the exponent determined above.