2 MONTH PLAN WEEK1 DAY 1
2^34-2^28
WHY CANT I SUBTRACT WHAT EXPONENT RULE IS USED HERE
There is no rule for subtracting two powers of the same base. x^a - x^b does not have a simple formula like x^a times x^b does. I would review the exponent rules to make sure you know how to apply them and when they apply.
In this case, they used the exponent rule (2^2)^17 = 2^(2*17) = 2^34 to create a case where we now have 2^34 - 2^28. They then factored out the greatest power of 2 they could from both terms to get 2^28(2^6 - 1). Then, we simplify the parentheses: 2^28(64 - 1) = 2^28(63) = 2^28 x 3^2 x 7. We get that the greatest prime factor is (D) 7.
Since we didn’t have a rule for difference of powers of the same number (i.e. 2^34 - 2^28), then we tried something else, specifically factoring.
I hope this helps!
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