Algebra: Chapter 5-1 and 5-2, p 204 and 209
Exponents and More with Exponents
Remember, an exponent tells how many times we use a base as a factor. For example, `a^3=a*a*a`. An expression written with exponents is written using exponential notation.
Rule 1: `a^0=1`
For like bases, we have:
- Rule 2, to multiply we do `a^m * a^n = a^(m+n)`
- Rule 3, to divide, we do `a^m/(a^n) = a^(m-n)`
Rule 4, for negative exponent, we can express them as positive by, `a^-m=1/(a^m)`
Rule 5, for raising a power to another power, `(a^m)^n = a^(mn)`
Rule 6, for raising a product to a power, `(ab)^n=a^n*b^n`
Rule 7, for raising a quotient to a power, `(a/b)^n=a^n/(b^n)`
Remember and MEMORIZE THESE RULES for Lessons 1 and 2. Practice here!
Math-8, Chapter 7-5, p 346
Solving Equations with Variables on Each Side
If there are variables on BOTH sides of the equal sign, then we have to move the variables ALL to one side BEFORE we begin solving the equality. We usually add or subtract variables first, then add/subtract constants, then finally, multiply/divide constants to solve for the variable.
For example,
`6 − 8x = 20x +20`
Add `8x` to both sides, giving us
`6 − 8x +8x= 20x +8x +20`, simplifying to
`6 = 28x +20`, from here we can do our STEP 1, and subtract 20 from both sides,
`6 − 20 = 28x + 20 − 20`, or
`−14 = 28x`, dividing by 28 to isolate the x, we have
`(−14/28) = (28/28)x` or finally
`−1/2 = x`, our answer!