Exponent Laws Review

• product of powers: a^x * a^y = a^(x + y)
• quotient of powers: (a^x)/(a^y) = a^(x - y)
• nroot(a) = a^(1/n)
• nroot(a^m) = a^(m/n)
• IMPORTANT NOTE: I forgot to include one law in the video which is also very important
  • power of a power: (a^x)^y = a^(x*y)

Solving Exponential Equations Algebraically

• if a^x = a^y, then x = y

Examples with Base 2

• write both sides with a common base if possible
  • if not possible, use a graphing calculator (or use logarithms, which you'll learn in the upcoming chapters)

Examples with Base 3

Examples with Base 6 and 7

Confirming the Solution to a Exponential Equation

• when you solved for x, plug in the x value(s) into the original equation
• if both sides of the equation are equal, your solution is correct

Solving an Exponential Equation Using a Graphing Calculator