Exponents Flashcards
When can I add or subtract exponents?
When the bases are the SAME
EX.
(10^4)*(10^3) = 10^7
The base is 10.
(Multiplication = ADD)
(Division = SUBTRACT)
Reverse this rule…how to factor 3 ^ ( a + 1 )?
3^a * 3^1
Anytime I see an exponent with an + or - sign, then use the same base and either X or Divide to factor it out.
Any number ^ 0 =
1
0 ^ Any number =
0 (Think about it…000*0 etc…)
When raising a fraction/decimal between (0 and 1) to an exponent, the value gets…?
Smaller
EX.
.75)(.75)(.75
-2^2 = 4?
NO It equals (-4)
4 would be the answer to this question
(-2)^2
It must be in the parenthesis.
Is this valid? (3/4)^1 = (3^1)/(4^1)
Yes
Is this valid? (12)^3 = (3*4)^3
Yes
When you raise an exponential term to an exponent, what operation should be used?
EX.
(4^3)^3
Multiplication
4^9
How can this expression be rewritten?
3^(4/3)
This equals the cubed root of 3^4.
The numerator is the power.
The denominator is the root.
How to factor and exponential expression.
EX.
3^10+3^8+3^4 = ?
(3^4)((3^6)+(3^4)+(1))
When a problem involves exponential expressions on both sides of the equation, it is imperative to rewrite the equation with the same bases or with the same exponents. Once the bases or exponents are the same, eliminate them and solve for the remainder of the problem.
EX - pg. 43 - Algebra
Fractions side by side, perform which operation?
45 4
_ X _
1 15
Multiplication
= 180/15
Is this valid? 4(3^3) = (12)^3
No!
This is in it’s simplest form.
When could you multiply the 4 into the (expression)?
If 4 had an exponent of 3 also.
(4^3)*(3^3) = (12)^3
Is this valid? (2^10) + (2^10) + (2^10) = 2^30
No!
It equals 4(2^10)
Factor Exponents…
How does this work [4(4y0] = (4^(y+1))
?
(333)^2 can also be written as ?
(3^3)^2 = 3^6
When you see What is the value of (8^3)(32^2)(16^-4) how do you solve?
Break down each into factors. Re-write exponents. Add exponents.
If both sides of an equation have exponential expressions, how can you solve?
Make the bases the same. Once that is complete, you can drop the basis and solve the exponents as the new equation.
When there are exponents in the problem, look to?
make the numbers have the same base
If exponential terms are being added, you have to?
solve for each term before adding (If the exponents are large, then there is usually some trick to simplify the exponents before solving.)