Exponents: division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}

Exponents: division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}

Basic concepts: Quotient rule of exponents,
Related concepts: Quotient rule,

Lessons

  • 1.
    prove: 8582=85−2=83{8^5 \over 8^2} = 8^{5-2} = 8^3
  • 2.
    simplify: 100a16b3c72a4c8{100a^{16}b^3c^7 \over 2a^4c^8}
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6.
Exponential and Logarithmic functions
6.1
Converting from logarithmic form to exponential form
6.2
Evaluating logarithms without calculator
6.3
Common logarithms
6.4
Evaluating logarithms using change-of-base formula
6.5
Converting from exponential form to logarithmic form
6.6
Product rule of logarithms
6.7
Quotient rule of logarithms
6.8
Combining product rule and quotient rule in logarithms
6.9
Solving logarithmic equations
6.10
Evaluating logarithms using logarithm rules
6.11
Continuous growth and decay
6.12
Finance: Compound interest
6.13
Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
6.14
Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
6.15
Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}
6.16
Exponents: Negative exponents
6.17
Exponents: Zero exponent: a0=1 a^0 = 1
6.18
Exponents: Rational exponents
6.19
Graphing exponential functions
6.20
Graphing transformations of exponential functions
6.21
Finding an exponential function given its graph
6.22
Logarithmic scale: Richter scale (earthquake)
6.23
Logarithmic scale: pH scale
6.24
Logarithmic scale: dB scale
6.25
Finance: Future value and present value
Precalculus
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