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In an expression like a^n:

a is called the base.

n is the exponent (or power).

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1. Any non-zero number to the power of 0 is equal to 1.

2. A negative exponent indicates taking the reciprocal. Put a^n in the denominator.

3. When a fraction is used as the base, a negative exponent causes the fraction to "flip". This is equivalent to swapping the numerator and the denominator and then removing the negative sign.

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1. An exponent of 1/n means taking the n-th root of the base.

2. The denominator n represents the root, and the numerator m represents the power.

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1. When the bases are the same, add the exponents.

2. A product raised to a power applies the exponent to each factor.

3. When dividing with the same base, subtract the exponents.

4. A power raised to another power means multiply the exponents.

5. A product raised to a power applies the exponent to each factor.

6. A negative exponent with a fraction flips the fraction and makes the exponent positive.

7. A negative exponent means take the reciprocal of the expression with a positive exponent.

8. The reciprocal of a negative power equals the positive power.

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Simplifying numerical and algebraic expressions involving exponents

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Simplifying numerical and algebraic expressions involving exponents

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1. Use the exponent rules and simplify the same way you would simplify numerical expressions

2. When using substitution, simplify the expression before substituting

3. When working with expressions involving radicals, simplify by changing the expression into exponential form and applying the exponent rules

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1. General equation: f(x) = bx where b≠0,1

2. First differences are related by multiplication Second differences are not constant

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Exponential growth/decay Domain and Range

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Exponential growth/decay Domain and Range

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1. The function increases rapidly as x increases. In the case |b|>1

2. The function decreases rapidly as x increases. In the case |b|<1

3. Domain: { xER }

4. Range: { y>0| yER }

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Given g(x)=ab^k(x-h)+c

1. hor. translation → d

2. hor. stretch or compression → the value of k

3. reflection in the y-axis → the sign of k

4. ver. stretch or compression → the value of a

5. reflection in the x-axis → the sign of a

6. ver. translation → c

Domain is not affected by transformations → stays as D:{xER}

Range: → if the transformed graph is above the asymptote y=c, R:{y>c/yER} → if the transformed graph is below the asymptote y=c, R: {y<c/yER}

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Given the equation f(x)=ab^x

f(x) - final amount or number

a: initial amount or number

b- exponential growth or decay

If there is growth, b=1 + growth rate

If there is decay, b=1 - decay rate

x - number of growth or decay

Be careful of the units