All ACT Math Resources
Example Question #1 : How To Find A Ratio Of Exponents
If and , then which of the following CANNOT be the value of ?
Even roots of numbers can either be positive or negative. Thus, x = +/- 5 and y = +/- 3. The possible values from x + y can therefore be:
(-5) + (-3) = -8
(-5) + 3 = -2
5 + (-3) = 2
5 + 3 = 8
Example Question #2 : How To Find A Ratio Of Exponents
If for all not equal to 0, which of the following must be true?
Since the problem states that , you can assume that
This shows that .
Example Question #1 : Exponential Ratios
If and are positive integers and , then what is the value of ?
43 = 64
Alternatively written, this is 4(4)(4) = 64 or 43 = 641.
Thus, m = 3 and n = 1.
m/n = 3/1 = 3.
Example Question #2 : Exponential Ratios
Write the following logarithm in expanded form:
Example Question #571 : Algebra
If and are both rational numbers and , what is ?
This question is asking you for the ratio of m to n. To figure it out, the easiest way is to figure out when 4 to an exponent equals 8 to an exponent. The easiest way to do that is to list the first few results of 4 to an exponent and 8 to an exponent and check to see if any match up, before resorting to more drastic means of finding a formula.
And, would you look at that. . Therefore, .