GMAT Math : Understanding exponents

Example Questions

Example Question #1124 : Problem Solving Questions

Give the sum in scientific notation:

Possible Answers:

Correct answer:

Explanation:

Rewrite the second addend as follows:

This is not in scientific notation; we adjust as follows:

Example Question #1125 : Problem Solving Questions

Give the quotient in scientific notation:

Possible Answers:

Correct answer:

Explanation:

Since 0.9375 does not fall in the range  , we adjust the answer as follows:

Example Question #23 : Exponents

Give the difference in scientific notation:

Possible Answers:

Correct answer:

Explanation:

Rewrite the second addend as follows:

Example Question #24 : Exponents

Express the product in scientific notation:

Possible Answers:

Correct answer:

Explanation:

Since 40 does not fall inside the rangle , we adjust the answer as follows:

Example Question #21 : Understanding Exponents

If , what does  equal?

Possible Answers:

Correct answer:

Explanation:

We can use the fact that  to see that

Since , we have

.

Example Question #26 : Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

Use the properties of exponents as follows:

Example Question #21 : Exponents

Solve for

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

The left and right sides of the equation have the same base, so we can equate the exponents and solve:

Example Question #1131 : Problem Solving Questions

Which of the following is equal to   ?

Possible Answers:

Correct answer:

Explanation:

We'll need to remember a few logarithmic properties to answer this question:

Now we can use these same rules to rewrite the log in question:

Example Question #1132 : Problem Solving Questions

Simplify the following expression:

.

Possible Answers:

Correct answer:

Explanation:

We start by simplifying the expression on the top. Let's add the exponents inside the parentheses and then multiply by the exponent outside of the parentheses.

Then we substract the denominator exponent form the numerator exponent:

Example Question #1133 : Problem Solving Questions

Simplify the following:

.

Possible Answers:

Correct answer:

Explanation:

First, we need to add the exponents of the elements with the same base that are multiplied, and subtract the exponents of same-base elements that are divided:

Then

Any value raised to the power of 0 equals 1 so the final result is 1.