All GMAT Math Resources
Example Questions
Example Question #11 :Understanding Powers And Roots
What is?
Example Question #12 :Understanding Powers And Roots
What is?
Example Question #13 :Understanding Powers And Roots
What is?
Example Question #14 :Understanding Powers And Roots
What is?
Example Question #11 :Understanding Powers And Roots
What is?
Example Question #16 :Understanding Powers And Roots
Which of the following is equivalent to?
Example Question #17 :Understanding Powers And Roots
The two terms have the same base, 3. Therefore, we add the exponents to simplify:
Example Question #18 :Understanding Powers And Roots
Find the remainder
很明显,we aren't expected to calculate 75^75. The clue is that since we are supposed to divide by 38, let's see if we can rewrite the numerator so that we have a 38 in it.
For example:,
and,
so we have:
If we expanded this expression, all of the terms but one will have ain them, so all of the terms except for the last term, when divided by, will not leave a remainder.
The last term will be, which is just.
Essentially, all we are asked to do is to figure out the remainder whenis divided by.
Otherwise stated:
, where R is the remainder.
很明显,
Example Question #19 :Understanding Powers And Roots
Give the area of the above kite.
The area cannot be determined from the information given.
,
so the lengths of the sides of each triangle comprise a Pythagorean triple. Therefore, each triangle is a right triangle with legs 7 and 24, and the kite is a composite of two such right triangles. Its area is therefore
Example Question #20 :Understanding Powers And Roots
Which of the following expressions is equivalent to?
You may assume thatis positive.
None of the other responses is correct.
For all integersand all positive bases,
by definition.
Set: