### All PSAT Math Resources

## Example Questions

### Example Question #531 : Algebra

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

**Possible Answers:**

**Correct answer:**

Explanation:

4^{3 }= 64

Alternatively written, this is 4(4)(4) = 64 or 4^{3 }= 64^{1.}

Thus, *m* = 3 and *n* = 1.

*m*/*n* = 3/1 = 3.

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

Write the following logarithm in expanded form:

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #231 : Exponents

Which of the following lists the above quantities from least to greatest?

**Possible Answers:**

II, III, I, IV

I, III, II, IV

IV, III, II, I

I, IV, II, III

I, IV, III, II

**Correct answer:**

I, III, II, IV

Explanation:

### Example Question #1 : Exponents And Rational Numbers

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation:

Since

Hence

### Example Question #2 : Exponents And Rational Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #3 : Exponents And Rational Numbers

Solve for :

**Possible Answers:**

**Correct answer:**

Explanation:

From the equation one can see that

Hence must be equal to 25.

### Example Question #4 : Exponents And Rational Numbers

Evaluate:

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #5 : Exponents And Rational Numbers

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #1 : Exponents And Rational Numbers

and

Find

**Possible Answers:**

**Correct answer:**

Explanation:

Hence the correct answer is .

### Example Question #1 : How To Find An Exponent From A Rational Number

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation:

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 .

Aaron

Certified Tutor

Certified Tutor

Portland State University, Bachelors, Economics. Portland State University, Masters, Environmental and Resource Management.

Matthew

Certified Tutor

Certified Tutor

Rider University, Bachelor of Science, Chemistry. Rutgers University-Camden, Master of Science, Organic Chemistry.

### All PSAT Math Resources

Popular Subjects

LSAT Tutors in Miami, MCAT Tutors in Seattle, Spanish Tutors in Chicago, SSAT Tutors in Chicago, Calculus Tutors in Miami, SSAT Tutors in Houston, Calculus Tutors in Los Angeles, GRE Tutors in Chicago, GMAT Tutors in San Diego, Chemistry Tutors in Denver
Popular Courses & Classes

GRE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Boston, SSAT Courses & Classes in Boston, ISEE Courses & Classes in Houston, SAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Denver, LSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Denver, SSAT Courses & Classes in Phoenix, SAT Courses & Classes in Atlanta