Describe how (2 cubed) (2 superscript negative 4) can be simplified.
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Suppose 
is the number of possible combinations for a suitcase with a lock consisting of 
wheels. If you added one more wheel onto the lock, there would only be 9 allowed possible digits you can use for the new wheel. This means the number of possible combinations for 
wheels, or 
is given recursively by the formula
starting with
(because you can start the combination with any one of the ten available digits 0 through 9).
For example, if the combination for a 3-wheel lock is 282, then a 4-wheel lock can be any one of 2820, 2821, 2823, ..., 2829 (nine possibilities depending on the second-to-last digit).
By substitution, you have
This means a lock with 55 wheels will have
possible combinations (a number with 53 digits).
starting with
For example, if the combination for a 3-wheel lock is 282, then a 4-wheel lock can be any one of 2820, 2821, 2823, ..., 2829 (nine possibilities depending on the second-to-last digit).
By substitution, you have
This means a lock with 55 wheels will have
possible combinations (a number with 53 digits).
The equivalent expressions are 2(24m + 21n) and 3(16m + 14n) and 6(8m + 7n)
<em><u>Solution:</u></em>
Given that, we have to factor the given expression
<em><u>Given expression is:</u></em>
48m + 42n
The equivalent expressions can be found by factoring out the common factors of 48 and 42
<em><u>Let us first find the factors of 48 and 42</u></em>
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Thus the common factors are: 1, 2, 3, 6
Let us factor out 2 from given expression
Now factor out 3 from given expression
Now factor out 6 from given expression
Thus the equivalent expressions are 2(24m + 21n) and 3(16m + 14n) and 6(8m + 7n)