Exponents: Mary Danielle M. Alcantara Mathematics Instructor Malcantara@nagahope - Edu.ph Elective 10: Calculus
Exponents: Mary Danielle M. Alcantara Mathematics Instructor Malcantara@nagahope - Edu.ph Elective 10: Calculus
Exponents: Mary Danielle M. Alcantara Mathematics Instructor Malcantara@nagahope - Edu.ph Elective 10: Calculus
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Laws of Exponents
•
6. 9.
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Laws of Exponents
• Quotient Rule
To divide two powers with the
same base, subtract the
exponents.
• Power of a Product Rule
To raise a quotient to a power,
raise the dividend and divisor to
the power.
Laws of Exponents
•
Example:
=
Laws of Exponents
• Can you simplify an expression
where an exponent has an
exponent? For example, how
would you simplify ?
Laws of Exponents
• Power of a Power Rule
To raise a power to a new power, multiply the exponents
Laws of Exponents
•
Example:
Laws of Exponents
• The Zero Exponent
•
Recall that
However, any quantity divided by itself is
If , then the following would be true:
equal to one. Therefore, , which means .
This is true in general:
if .
Laws of Exponents
– If the term is a factor in the
• The Negative Exponent
• numerator with a negative exponent,
;
write it in the denominator with a
– If a term has a negative exponent,
positive exponent.
write it as 1 over the term with a
positive exponent.
– If a term has a negative exponent, – If the term is a factor in the
write the reciprocal with a positive denominator with a negative
exponent. exponent, write it in the numerator
with a positive exponent.
Laws of Exponents
•
Example:
Solving Exponential Equations
•
Exponential equations are equations in which variables occur as exponents.
For example, exponential equations are in the form .
To solve exponential equations with same base, use the property of equality of
exponential functions.
𝒙= 𝟒
𝟏𝟓
Solving Exponential Equations
•
Example6: Evaluate Example5: Solve the equation .
Solution
Solution
Solving Exponential Equations
• the value of .
Solve
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Solving Exponential Equations
•
1. 3.
5.
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Solving Exponential Equations
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6.
Solving Exponential Equations
•
Solve for the value of .