PSAT Math : How to find patterns in exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #1 : How To Find Patterns In Exponents

If ax·a4 = a12 and (by)3 = b15, what is the value of x - y?

Possible Answers:

-9

-2

6

3

-4

Correct answer:

3

Explanation:

Multiplying like bases means add the exponents, so x+4 = 12, or x = 8.

Raising a power to a power means multiply the exponents, so 3y = 15, or y = 5.

x - y = 8 - 5 = 3.

Example Question #1 : How To Find Patterns In Exponents

If p and q are positive integrers and 27= 9q, then what is the value of q in terms of p?

Possible Answers:

p

(3/2)p

(2/3)p

3p

2p

Correct answer:

(3/2)p

Explanation:

The first step is to express both sides of the equation with equal bases, in this case 3. The equation becomes 33p = 32q. So then 3p = 2q, and q = (3/2)p is our answer. 

Example Question #2 : How To Find Patterns In Exponents

Simplify 272/3.

Possible Answers:

3

9

27

125

729

Correct answer:

9

Explanation:

272/3 is 27 squared and cube-rooted. We want to pick the easier operation first. Here that is the cube root. To see that, try both operations. 

272/3 = (272)1/3 = 7291/3 OR

272/3 = (271/3)2 = 32

Obviously 32 is much easier. Either 32 or 7291/3 will give us the correct answer of 9, but with 32 it is readily apparent. 

Example Question #1237 : Psat Mathematics

If  and  are integers and 

 

what is the value of ? 

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we will have to take the log of both sides to bring down our exponents. By doing this, we will get \dpi{100} \small a\ast log\left (\frac{1}{3} \right )= b\ast log\left ( 27 \right ).

To solve for \dpi{100} \small \frac{a}{b} we will have to divide both sides of our equation by \dpi{100} \small log\frac{1}{3} to get \dpi{100} \small \frac{a}{b}=\frac{log\left ( 27 \right )}{log\left ( \frac{1}{3} \right )}.

\dpi{100} \small \frac{log\left ( 27 \right )}{log\left ( \frac{1}{3} \right )} will give you the answer of –3.

Example Question #1238 : Psat Mathematics

If and , then what is ?

Possible Answers:

Correct answer:

Explanation:

We use two properties of logarithms: 

log(xy) = log (x) + log (y)

log(x^{n}) = nlog (x)

So

Example Question #1239 : Psat Mathematics

Evaluate:

x^{-3}x^{6}

Possible Answers:

x^{-18}

x^{3}

x^{-3}

x^{9}

x^{6}

Correct answer:

x^{3}

Explanation:

x^{m}\ast x^{n} = x^{m + n}, here  and , hence .

Example Question #2 : How To Find Patterns In Exponents

Solve for

\left ( \frac{2}{3} \right )^{x+1} = \frac{27}{8}

Possible Answers:

None of the above

Correct answer:

Explanation:

\left ( \frac{2}{3} \right )^{x+1} = \frac{27}{8} = \left ( \frac{3}{2} \right )^{3} = \left ( \frac{2}{3} \right )^{-3}

  which means

Example Question #1242 : Psat Mathematics

Which of the following statements is the same as:

Possible Answers:

Correct answer:

Explanation:

Remember the laws of exponents. In particular, when the base is nonzero:

An effective way to compare these statements, is to convert them all into exponents with base 2. The original statement becomes:

This is identical to statement I. Now consider statement II:

Therefore, statement II is not identical to the original statement. Finally, consider statement III:

which is also identical to the original statement. As a result, only I and III are the same as the original statement. 

Example Question #2 : How To Find Patterns In Exponents

Write in exponential form:

Possible Answers:

Correct answer:

Explanation:

Using properties of radicals e.g.,

we get

Example Question #2 : How To Find Patterns In Exponents

Write in exponential form:

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

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