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Example Questions
Example Question #2401 : Sat Mathematics
Evaluate:
The expression is undefined
is defined to be equal to
for any real or imaginary
and for any real
; therefore,
To evaluate a positive power of , divide the power by 4 and note the remainder:
Therefore,
Substituting,
Rationalizing the denominator by multiplying both numerator and denominator by :
Example Question #1 : How To Find An Exponent From A Rational Number
Solve for .
Since
Hence
Example Question #2 : How To Find An Exponent From A Rational Number
Simplify:
Example Question #3 : How To Find An Exponent From A Rational Number
Solve for :
From the equation one can see that
Hence must be equal to 25.
Example Question #4 : How To Find An Exponent From A Rational Number
Evaluate:
Example Question #1 : Exponents And Rational Numbers
Solve for .
Example Question #6 : How To Find An Exponent From A Rational Number
and
Find
Hence the correct answer is .
Example Question #1 : Exponents And Rational Numbers
Solve for .
Use the rules of logarithms to combine terms.
Hence,
By fatoring we get
Hence .
However, you cannot take the logarithm of a negative number. Thus, the only value for is
.
Example Question #2 : Exponents And Rational Numbers
If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?
40
125
27
36
12
27
The answer is 33 = 27
Example Question #1 : How To Find An Exponent From A Rational Number
Solve for .
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