Day 73 – December 12

Algebra: Chapter 5, Lesson 1, page 204.

Exponents!

Exponents and More with Exponents

Remember, an exponent tells how many times we use a base as a factor. For example, ${\displaystyle a^3=a\cdot a\cdot a}$. An expression written with exponents is written using exponential notation.

For like bases, we have:

1. Rule: ${\displaystyle a^0=1}$
2. Rule: to multiply we do ${\displaystyle a^m\cdot a^n=a^{m+n}}$
3. Rule: to divide, we do ${\displaystyle \frac{a^m}{a^n}=a^{m-n}}$
4. Rule: for negative exponent, we can express them as positive by, ${\displaystyle a^{-m}=\frac{1}{a^m}}$
5. Rule: for raising a power to another power, ${\displaystyle {\left(a^m\right)}^n=a^{mn}}$
6. Rule: for raising a product to a power, ${\displaystyle {\left(ab\right)}^n=a^n\cdot b^n}$
7. Rule: for raising a quotient to a power, ${\displaystyle {\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n}}$

Remember and MEMORIZE THESE RULES for Lessons 1 and 2. Practice here!

They are also included in the Algebra Cheat Sheet that was passed today. As long as you remember these 7 formulae, you’ll be OK. Remember, if you forget the rules, just write out the problem and see what can be simplified!

PurpleMath has an EXCELLENT 2 page tutorial, click here!

Two of tonight’s homework problems solved by MrE are here! Just click it.

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Algebra 1a: Chapter 4, Lesson 1, page 172.

Inequalities and Their Graphs

Symbols:

• , is less than
• ${\displaystyle \le }$, is less than or equal to
• ${\displaystyle >}$, is greater than
• ${\displaystyle \ge }$, is greater than or equal to

Open or closed circles on the number line:

• OPEN CIRCLE  (get as close to the value BUT don’t touch) it for or ${\displaystyle >}$
• CLOSED CIRCLE (included the value on the number line) for ${\displaystyle \le }$ or ${\displaystyle \ge }$