Multiply powers: unequal base and unequal exponent
When multiplying potencies, a task actually crept in that was so without Further things cannot be solved, because with an unequal base and an unequal exponent it is possible actually nothing.
What you need:
- Basic rules of power calculation
Multiply powers - short info
- Most students know the power laws, at least in terms of their wording. According to them, it is particularly easy if there is an unequal exponent but the same base: You simply add the exponents as in a4* a7 = a11.
- The task of multiplying the same exponents with one another when the base is not the same is still successful easy, because the two bases simply multiply, the exponents are retained as in b6 * a6 = (from)6. This calculation step could also be called "summarizing".
- However, there are tasks that have unequal exponents and unequal bases, such as am * bn not solvable in the sense of "multiply" or "summarize".
Unequal base and unequal exponent - these tips will help
In some cases, however, you can use arithmetic tricks to ensure that the exercise has the same base or the same exponent. Here are two examples:
- The task (2x)5 * (3x)3 seems unsolvable at first (unequal base, unequal exponents), but you can still multiply or Summarize potencies by one Counting and letter (here the "x") treated separately: (2x)5 * (3x)3 = 25 * x5 * 33 * x3 = 32 * 27 * x8 = 864 * x8. Also pure number problems like (32)3 * (8)2 can be treated in this way (the basis here is the "2").
- Even with the simple example (x3)4 * (y2)6 it works with the expansion. First you solve the overarching powers (brackets) and get x12 * y12 = (xy)12.
Performing a square calculation - made easy
When you do a square calculation, it means to you that with numbers ...
Conclusion: not always such a thing Potencies multiply, but for some tasks you have to use such arithmetic tricks.
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