EXPONENT
LAWS
#1 Makamae Aquino
Period 2A
6 LAWS OF EXPONENTS
- Negative Expo
- First Power
- Zero Power
- MA
- DS
- PM
NEGATIVE EXPONENT LAW
-Negative exponents express small numbers.
-Law: Take base of negative exponent, flip its
location (numerator/denominator) & take away
negative sign of exponent.
FIRST POWER LAW
-When a number is raised to the power of
one.
-Law: when a number is raised to the
power of one, the number is itself.
ZERO POWER LAW
-When a number is raised to the power of
zero.
-Law: when a number is raised to the power
of zero, it is one.
MADSPM
MA= Multiply same base &
Add expo
DS= Divide same base
&
Subtract expo
PM= Power of a power
&
Multiply expo
MA LAW
-Used when multiplying
-Law: When multiplying exponent
numbers with the same base, add
exponent.
STEP ONE- COEFFICIENTS &
BASES
Problem: 5 x to the fourth multiplied by 3 x to the third.
Multiply the coefficients (if coefficients are the same, just
drop them).
Drop the base/bases (variable).
5 multiplied by 3 is 15.
Bring down the x.
STEP TWO- EXPONENTS
Problem: 5 x to the fourth multiplied by 3 x to the third.
Add the exponents (ex. x to the sixth and x to the eighth = x6+8).
x4+3=x7
STEP THREE- SIMPLIFY
Problem: 5 x to the fourth multiplied by 3 x to the third.
Put everything together.
Final Answer: 15x7
DS LAW
-Used when dividing
-Law: Dividing same base number,
subtract exponent (subtract
bottom from top)
STEP ONE- COEFFICIENTS &
BASES
Problem: 4 to the 5th power divided by 12 squared.
-Drop the coefficients and bases one by one by one (if the coefficients are the
same, drop the coefficients. If the coefficients are not the same, simplify them
[keep # on top, on the top and # on bottom, on the bottom])
Drop the base (variables). Keep the base on top, on the top, and base on
bottom, on the bottom.
4 and 12 is simplified to 1 and 3
STEP TWO- EXPONENTS
Problem: 4 to the 5th power divided by 12 squared
Bring the exponents down to the
numerator (1) and subtract them
(5 - 2).
New Answer: 1 to 5-2 divided by 3
STEP THREE- SIMPLIFY
Problem: 4 to the 5th power divided by 12 squared
Simplify the new answer (1 to the 5-2 divided by 3).
5-2=3. 1x1x1=1
Final answer: 1 (numerator) divided by 3
(denominator)= 3
PM LAW
-Used when figuring out a power of a power.
-Law: Taking a power of a power, and
multiplying the exponents.
STEP ONE- MULTIPLYING COEFFICIENTS
Problem: (-2 multiplied by x to the seventh) to the fourth.
Drop the coefficient down and multiply.
*Everything in the () needs to be multiplied. If the number has no
exponent, multiply the coefficient by the exponent. If there is an
exponent with the coefficient, multiply the exponent by the exponent
outside the ().
-2 multiplied by four=16. (The exponent is even, therefore the
coefficient becomes positive).
STEP TWO- MULTIPLYING EXPONENTS
Problem: (-2 multiplied by x to the seventh) to the fourth.
Drop the variables and their exponents.
Multiply all the variable’s exponents by the exponent outside the
().
x to the seventh multiplied by 4=28
STEP THREE- SIMPLIFY
Problem: (-2 multiplied by x to the seventh) to the fourth.
Put everything together for the final answer.
Final answer: 16 and x28= 16x to the 28.