ACT Math : How to find a ratio of exponents

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : How To Find A Ratio Of Exponents

If  and , then which of the following CANNOT be the value of ?

 

Possible Answers:

Correct answer:

Explanation:

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 : Exponential Ratios

If  for all \dpi{100} \small n not equal to 0, which of the following must be true?

Possible Answers:

\dpi{100} \small y-x = 6

\dpi{100} \small \frac{y}{x} = 6

\dpi{100} \small yx = 6

\dpi{100} \small y+x = 6

\dpi{100} \small \frac{x}{y} = 6

Correct answer:

\dpi{100} \small y-x = 6

Explanation:

Remember that \dpi{100} \small \frac{n^{y}}{n^{x}}=n^{y-x}

Since the problem states that , you can assume that \dpi{100} \small n^{y-x}=n^{6}

This shows that \dpi{100} \small y-x = 6.

Example Question #1 : How To Find A Ratio Of Exponents

If  and are positive integers and , then what is the value of ?

Possible Answers:

Correct answer:

Explanation:

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 : How To Find A Ratio Of Exponents

Write the following logarithm in expanded form:

 

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : How To Find A Ratio Of Exponents

If  and  are both rational numbers and , what is ?

Possible Answers:

Correct answer:

Explanation:

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, .

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: