SAT Math : Pattern Behaviors in Exponents
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Example Question #274 : Exponents
Express 
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 #275 : Exponents
Solve for 
This statement has no solution.
This statement has no solution.
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 #276 : Exponents
Solve for 
The equation has no solution.
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 #691 : Algebra
What is the unit's digit of 
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,
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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