3 The laws you used in the warm up with integer bases apply to all bases, even variable bases. The laws also apply for all types of exponents, including fractions and decimals. Let’s review the rules and see them applied.
4 Labeling an exponential expression The expression is written and read as X to the 5th power.X is called the base of the expression.5 called a power or exponent for the expression.The exponent, 5, tells us that we want X multiplied with its self 5 timesPower or exponential form is X5x x x x x is Expanded form
5 Practice Identify the base of Identify the exponent of Is in exponential or expanded form?
6 ZERO POWER RULEAny base(s) raised to the zero power will always equal 1. Examples
10 Power of a PowerWhen we have an exponent raised to an exponent we multiple the exponents. Example If there are numbers or more than one variable, inside the parenthesis, they all get raised to the outside power. When we have we first simplify by ‘distributing’ the outside exponent inside, and then, since the two groups are multiplied, we added the exponents of like bases. Examples
17 Negative ExponentsIf we have a negative exponent we can write it as a positive by taking the reciprocal. If the negative exponent is on the top of a fraction we can write it positive by simply moving it to the bottom of the fraction. If the negative exponent is on the bottom of a fraction we can write it positive by moving it to the top of the fraction. Examples