How to find an exponent from a rational number
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GRE Quantitative Reasoning › How to find an exponent from a rational number
Solve for .
Explanation
The bases don't match.
However:
and we recognize that
.
Anything raised to negative power means over the base raised to the postive exponent.
.
Solve for .
Explanation
Since we can write .
With same base we can set up an equation of
Divide both sides by and we get
.
Solve for .
Explanation
can be written as
Since there is a common base of , we can say
or
.
Solve for .
Explanation
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, .
.
Solve for
Explanation
Recall that .
With same base, we can write this equation:
.
By subtracting on both sides,
.
Compare and
.
The relationship cannot be determined from the information given.
Explanation
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.
Solve for .
Explanation
We still don't have the same base however:
Then,
.
With same base we can set up an equation of .
Divide both sides by and we get
.
Solve for .
Explanation
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
.
Solve for .
Explanation
They don't have the same base, however: .
Then . You would multiply the
and the
instead of adding.
.
Solve for .
Explanation
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 .