SAT Math : Pattern Behaviors in Exponents

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #688 : Algebra

Express  in terms of .

Possible Answers:

Correct answer:

Explanation:

To solve this problem, first convert all numbers to have the like base of five.

Recall the rule of exponents which states, when multiplying like bases we add their exponents.

Since we have the same base we can set the exponents equal to each other and solve.

Example Question #689 : Algebra

Solve for :

Possible Answers:

This statement has no solution.

Correct answer:

This statement has no solution.

Explanation:

To solve this problem, first convert all numbers to have the like base of two

Recall that when exponents are raised to another power the exponents are multiplied together.

Since we have the same base we can set the exponents equal to each other and solve.

This statement is identically false, so the original statement has no solution.

Example Question #21 : How To Find Patterns In Exponents

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

To solve this problem, first convert all numbers to have the like base of three.

Since we have the same base we can set the exponents equal to each other and solve.

Example Question #31 : Pattern Behaviors In Exponents

What is the unit's digit of ?

Possible Answers:

Correct answer:

Explanation:

Notice that there is a repeating pattern in the unit's digit of the powers of 2:

and so on. The pattern is four numbers long, which means we need to count how many complete blocks of 4 numbers are in the 357-number pattern. That is,

 with a remainder of 1.

The remainder is all we need, since it tells us where in the pattern we need to be: the first place, with a unit's digit of 2.

 

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