Day 96 – Exponential Rules review

Vocabulary Base - the value that is raised to a power when a number is written in exponential notation In the tone 53, 5 is the base and 3 is the exponent. Exponent - the value that indicates the number of times another value is multiplied by itself in exponential rotator The exponent, also called the power, is written in superscript In the term 53, 5 is the base and 3 is the exponent. Exponential notation - a condensed way of expressing repeated multiplication of a value by itself Exponential notation consists eta base and an exponent In the exponential term 53, 5 is the base and 3 is the exponent This is a shorthand way of wring 5*5*5. Also called exponential form

Power - a way of describing the exponent in exponential notation We can say the base is raised to the power of the exponent. For example we read x5 as "x raised to the 5th power.“ power of a power - raising a value written in exponential notation to a power as in (x2)3 product of powers - multiplication of two or more values in exponential form that have the same base—the base stays the same and the exponents are added. quotient of powers - division of two or more values in exponential form that have the same base—the base stays the same and the exponent in the denominator is subtracted from the exponent in the numerator

Zero-Exponent Rule: a0 =1. this says that anything raised to the zero power is 1.

Power Rule (Powers to Powers): (am)n = amn . This says that to raise a power to a power you need to multiply the exponents. There are several other rules that go along with the power rule, such as the product-to-powers rule and the quotient-to-power rule.

Negative Exponent Rule: this says the negative exponents in the numerator get moved to the denominator and become positive exponents. Negative exponents in the denominator get moved to the numerator and become positive exponents. Only move the negative exponents.

Product Rule: am  an = am+n. this says that to multiply two exponents with the same base. You keep the base and add the powers.

Quotient Rule: ,this says that to divide two exponents with the same base, you keep the base and subtract the powers. This is similar to reducing fractions; when you subtract the powers put the answer in the numerator or denominator depending on where the higher power was located. If the higher power is in the denominator, put the difference in the denominator and vice versa, this will help avoid negative exponents.

Example Simplify Rewrite as a product of fractions Rewrite variables with negative powers following the rule for negative exponents: a-n = Simplify division by a fraction Multiply fractions ANSWER

Example 2 Simplify

Example 3 Use the one to one property to solve for the variable. 1. 2.

Example 3 Use the one to one property to solve for the variable. 3.

Answer Use the one to one property to solve for the variable. 1. 2.

Answer Use the one to one property to solve for the variable. 3.