All GRE Math Resources
Example Questions
Example Question #22 :Algebra
find x
8x=2x+6
2 or -1
-1
2
4
3
3
8 = 23
(23)x= 23x
23x= 2x+6<- when the bases are the same, you can set the exponents equal to each other and solve for x
3x=x+6
2x=6
x=3
Example Question #23 :Algebra
Compareand.
The relationship cannot be determined from the information given.
First rewrite the two expressions so that they have the same base, and then compare their exponents.
Combine exponents by multiplying:
This is the same as the first given expression, so the two expressions are equal.
Example Question #1 :Exponents And Rational Numbers
Solve for.
can be written as
Since there is a common base of, we can say
or.
Example Question #1 :Exponents And Rational Numbers
Solve for.
The basees don't match.
However:
thus we can rewrite the expression as.
Anything raised to negative power meansover the base raised to the postive exponent.
So,..
Example Question #3 :Exponents And Rational Numbers
Solve for.
The bases don't match.
However:
and we recognize that.
Anything raised to negative power meansover the base raised to the postive exponent.
.
Example Question #31 :Algebra
Solve for
Recall that.
With same base, we can write this equation:
.
By subtractingon both sides,.
Example Question #4 :Exponents And Rational Numbers
Solve for.
Sincewe can rewrite the expression.
With same base, let's set up an equation of.
By subtractingon both sides, we get.
Take the square root of both sides we get BOTHand.
Example Question #33 :Algebra
Solve for.
They don't have the same base, however:.
Then. You would multiply theand theinstead of adding.
.
Example Question #1 :Exponents And Rational Numbers
Solve for.
There are two ways to go about this.
Method
They don't have the same bases however:. Then
You would multiply theand theinstead of adding. We have
Divideon both sides to get.
Method:
We can change the base fromto
This is the basic property of the product of power exponents.
We have the same base so basically.
Example Question #6 :Exponents And Rational Numbers
Solve for.
Since we can write.
With same base we can set up an equation of
Divide both sides byand we get.