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Example Questions
Example Question #21 : Algebra
find x
8x=2x+6
3
2 or -1
-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 #1 : 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 #3 : Exponents And Rational Numbers
Solve for
.
can be written as
Since there is a common base of
, we can sayor .
Example Question #25 : Algebra
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 #2 : Exponents And Rational Numbers
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 #31 : Algebra
Solve for
Recall that
.With same base, we can write this equation:
.
By subtracting
on both sides, .
Example Question #6 : How To Find An Exponent From A Rational Number
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 #3 : 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 #4 : Exponents And Rational Numbers
Solve for
.
There are two ways to go about this.
Method
They don't have the same bases however:
. ThenYou would multiply the
and the instead of adding. We haveDivide
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 #8 : Exponents And Rational Numbers
Solve for
.
Since we can write
.With same base we can set up an equation of
Divide both sides by
and we get .All GRE Math Resources
