Refrain: Exponents count how many times something is multiplied by itself.
$x^n=x \cdot x \cdot x \cdot \ldots \cdot x$
$(\mbox{ }\mbox{ }\mbox{ })^n=(\mbox{ }\mbox{ }\mbox{ }) \cdot (\mbox{ }\mbox{ }\mbox{ }) \cdot (\mbox{ }\mbox{ }\mbox{ }) \cdot \ldots \cdot (\mbox{ }\mbox{ }\mbox{ })$
Refrain: Exponents count how many times something is multiplied by itself.
Example: Write $(-3)^5$ in expanded form.
Example: Write $5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$ using exponent notation.
Example: Write $5 + 5 + 5 + 5 + 5 + 5 + 5 + 5$ using a shorthand notation.
Refrain: Exponents count how many times something is multiplied by itself.
Example: Write $\theta^4 \xi^2$ in expanded form.
Example: Write $x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot $ using exponent notation.
Refrain: Exponents count how many times something is multiplied by itself.
Example: Evaluate the expression $(-\frac{3}{4})^3$.
Example: Evaluate the expression $(-1)^{2178}$.
Example: Evaluate the expression $-1^{2178}$.
Example: Evaluate the expression $0^{1089}$.
Refrain: Exponents count how many times something is multiplied by itself.
Example: Write the expression $(\alpha+\beta)^3$ in expanded form.
Example: Write the expression $(v+w)(v+w)(v+w)(v+w)(v+w)$ in exponential form.
Order of Operations
On its own, is there any ambiguity to the statement $2+3 \cdot 5$?
Order of Operations
Step 1 Start with the expression within the innermost pair of grouping symbols.
Step 2 Perform all exponentiations.
Step 3 Perform all multiplications and divisions as they appear from left to right.
Step 4 Perform all additions and subtractions as they appear from left to right.
Some examples of grouping symbols: $()$, $[]$, $\{\}$, $\sqrt{\mbox{ }}$ $||$, fraction bars.
Order of Operations
Example: Use the order of operations to evaluate $5 \cdot 8 - 12 \div 3 + 1$.
Example: Use the order of operations to evaluate $$|7+(-1)|\cdot \sqrt{63+1}-(-5)$$
Example: Use the order of operations to evaluate $$\frac{8+(4-(-3)) \cdot 2}{-5+9-(-6) \cdot (-9)}$$
The Distributive Property
$a(b+c)=ab+ac$
Verify that $2 \cdot (3+5)$ is the same number as $2\cdot 3 + 2 \cdot 5$
The Distributive Property
With the distributive property, we can change the form of expressions.
Example: Rewrite the expression $(8a−2)(-2)$ using the distributive property.
The Distributive Property
The distributive property also allows us to combine like terms!
Example: Use the distributive property to combine like terms $$3\gamma + 8 \gamma$$