JulianMathHelp
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If multiplying two by itself two times the same as repeatedly multiplying 2 three times or two times? Also, is repeatedly multiplying 2 three times 2x2x2 or 2x2x2x2?
Exponents
- Thread starter JulianMathHelp
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This is why we use math notation. Natural languages are rife with ambiguity.
If I multiply two by itself once, I have
[MATH]2 \times 2 = 4.[/MATH]
If I multiply the result of multiplying two by itself twice I have
[MATH](2 \times 2) \times (2 \times 2) = 4 \times 4 = 16.[/MATH]
The English is obscure. The math is not.
JulianMathHelp
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So would 2 x 2 x 2 x 2 be repeatedly multiplying "2" four times or three times?
JulianMathHelp
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I am not exactly sure, but I would answer 4 times?
Steven G
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You are thinking too much. If I asked you how many numbers were being multiplied would you still say 4?
I guess that we just need to give you the answer. Since there are 5 2's that are being multiplied then the answer is 5.
Just count the number of two's there are and you will be correct every time.
The problem is that you have been taught a stupid way to define exponents.
[MATH]a^0 = 1.[/MATH]
[MATH]n > 0 \implies a^n = a * a^{(n-1)}.[/MATH]
So
[MATH]a^0 = 1.[/MATH]
[MATH]a^1 = a * 1 = a[/MATH]
[MATH]a^2 = a * a[/MATH]
[MATH]a^3 = a * (a * a) = a * a * a[/MATH]
[MATH]a^4 = a * (a * a * a) = a * a * a * a[/MATH]
That's it.
[MATH]a^0 = 1.[/MATH]
[MATH]n > 0 \implies a^n = a * a^{(n-1)}.[/MATH]
So
[MATH]a^0 = 1.[/MATH]
[MATH]a^1 = a * 1 = a[/MATH]
[MATH]a^2 = a * a[/MATH]
[MATH]a^3 = a * (a * a) = a * a * a[/MATH]
[MATH]a^4 = a * (a * a * a) = a * a * a * a[/MATH]
That's it.
JulianMathHelp
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So you could say that 2 is being repetedly multiplied 5 times?