SAT Math : SAT Mathematics
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Example Questions
Example Question #153 : Exponents
Solve:
When dividing expressions with the same variable, combine terms by subtracting the exponents, while leaving the variable unchanged. For this problem, we do that by subtracting 11-16, to get a new exponent of -5. However, because the exponent is negative, we can place the new expression in the denominator of the fraction and make the exponent positive:
Example Question #154 : Exponents
Simplify:
When dividing exponents, we subtract the exponents and keep the base the same.
Example Question #153 : Exponential Operations
Simplify:
When dividing exponents, we subtract the exponents and keep the base the same.
Example Question #46 : How To Divide Exponents
Simplify:
Although the bases aren't the same, we know that 
Therefore
We can now divide the exponents.
Example Question #5 : Exponential Operations
The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is 
Now, we can cancel out the 
Example Question #570 : Algebra
If
and
what is the value of a?
When dividing exponents,
Therefore,
If 
We can now solve the system of equations 
If we solve for a in the first equation and plug it into the second equation, we get 
If we substitute this value of b into the first equation, we can solve for a and find that 
Example Question #1 : Exponents And The Distributive Property
Factor 2x2 - 5x – 12
(x - 4) (2x + 3)
(x + 4) (2x + 3)
(x + 4) (2x + 3)
(x – 4) (2x – 3)
(x - 4) (2x + 3)
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
Example Question #2341 : Sat Mathematics
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
The relationship cannot be determined from the information given
Quantity B is greater
Quantity A is greater
The two quantities are equal
Quantity B is greater
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Example Question #1 : Exponents And The Distributive Property
Solve for all real values of 
First, move all terms to one side of the equation to set them equal to zero.
All terms contain an 
Now, we can factor the quadratic in parenthesis. We need two numbers that add to 
We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.
Our answer will be 
Example Question #2342 : Sat Mathematics
Find the product in terms of 
This question can be solved using the FOIL method. So the first terms are multiplied together:
This gives:
The x-squared is due to the x times x.
The outer terms are then multipled together and added to the value above.
The inner two terms are multipled together to give the next term of the expression.
Finally the last terms are multiplied together.
All of the above terms are added together to give:
Combining like terms gives
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