Chapter 7: Exponential Functions 7.1 & 7.2 Laws of Exponents Zero and Negative Exponents

The Product Rule When multiplying exponential expressions with the same base, add the exponents.

Multiply each expression using the product rule

Multiply each expression using the product rule

Multiply each expression using the product rule

The Quotient Rule When dividing exponential expressions with the same non-zero base, subtract the exponents.

Divide each expression using the quotient rule

Divide each expression using the quotient rule

Divide each expression using the quotient rule

Zero as an exponent Any real number (other than zero) raised to the zero power is 1. Show b^4/b^4

The Negative-Exponent Rule Show this: b^3/b^5

Use the negative-exponent rule to write each expression with a positive exponent.

Use the negative-exponent rule to write each expression with a positive exponent.

Use the negative-exponent rule to write each expression with a positive exponent.

The Power Rule (Powers to Powers) When an exponential expression is raised to a power, multiply the exponents.

Simplify each expression using the power rule

Simplify each expression using the power rule

Simplify each expression using the power rule

Products to Powers When a product is raised to a power, raise each factor to that power.

Simplify

Simplify

Quotients to Powers When a quotient is raised to a power, raise the numerator and denominator to that power, divide to simplify if necessary

Simplify

Simplify

Simplifying Exponential Expressions An exponential expression is ___________ when: No parenthesis appear No powers are raised to powers Each base occurs only once No negative or zero exponents appear Note: Simplify in this order!

Simplify

Simplify

Simplify

Simplify

Homework Exercise Set P.3 #1 – 63 odd