Exponents
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ACT Math › Exponents
Which of the following is the square of ?
You may assume both and
are positive.
Explanation
Use the square of a sum pattern, substituting for
and
for
in the pattern:
or
If an account has interest compounded quarterly at an annual rate of , what is the balance of the account after
years of compounding if the initial balance is
? Round to the nearest cent.
Explanation
Recall that the equation for compounded interest (with quarterly compounding) is:
Where is the balance,
is the rate of interest,
is the number of years, and
is the number of times it is compounded per year.
Thus, for our data, we need to know:
This is approximately .
If , then
Cannot be determined
Explanation
Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.
What is the value of m where:
-2
1
2
4
6
Explanation
If n=4, then 64(4/12)=64(1/3)=4. Then, 4=m4(1+m)/(m+4). If 2 is substituted for m, then 4=24(1+2)/(2+4)=241/2=2√4=22=4.
can be written as which of the following?
A.
B.
C.
A, B and C
B and C
A and C
C only
B only
Explanation
C is computing the exponent, while A and B are equivalent due to properties of fractional exponents.
Remember that...
Simplify the following:
Explanation
When two variables with exponents are multiplied, you can simplify the expression by adding the exponents together. In this particular problem, the correct answer is found by adding the exponents 5 and 5, yielding .
can be written as which of the following?
A.
B.
C.
A, B and C
B and C
A and C
C only
B only
Explanation
C is computing the exponent, while A and B are equivalent due to properties of fractional exponents.
Remember that...
Which of the following is the square of ?
You may assume both and
are positive.
Explanation
Use the square of a sum pattern, substituting for
and
for
in the pattern:
or
If an account has interest compounded quarterly at an annual rate of , what is the balance of the account after
years of compounding if the initial balance is
? Round to the nearest cent.
Explanation
Recall that the equation for compounded interest (with quarterly compounding) is:
Where is the balance,
is the rate of interest,
is the number of years, and
is the number of times it is compounded per year.
Thus, for our data, we need to know:
This is approximately .
Solve for :
Explanation
First, reduce all values to a common base using properties of exponents.
Plugging back into the equation-
Using the formula
We can reduce our equation to
So,