All GRE Math Resources
Example Questions
Example Question #21 : Exponents
find x
8x=2x+6
-1
3
2 or -1
4
2
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 #2 : Exponents And Rational Numbers
Compare and
.
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 #21 : Algebra
Solve for .
can be written as
Since there is a common base of , we can say
or
.
Example Question #4 : Exponents And Rational Numbers
Solve for .
The basees don't match.
However:
thus we can rewrite the expression as
.
Anything raised to negative power means over the base raised to the postive exponent.
So, .
.
Example Question #22 : Algebra
Solve for .
The bases don't match.
However:
and we recognize that
.
Anything raised to negative power means over the base raised to the postive exponent.
.
Example Question #1 : Exponents And Rational Numbers
Solve for
Recall that .
With same base, we can write this equation:
.
By subtracting on both sides,
.
Example Question #7 : Exponents And Rational Numbers
Solve for .
Since we can rewrite the expression.
With same base, let's set up an equation of .
By subtracting on both sides, we get
.
Take the square root of both sides we get BOTH and
.
Example Question #8 : Exponents And Rational Numbers
Solve for .
They don't have the same base, however: .
Then . You would multiply the
and the
instead 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 the and the
instead of adding. We have
Divide on both sides to get
.
Method :
We can change the base from to
This is the basic property of the product of power exponents.
We have the same base so basically .
Example Question #1 : How To Find An Exponent From A Rational Number
Solve for .
Since we can write .
With same base we can set up an equation of
Divide both sides by and we get
.
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