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Order of Arithmetric Operations |
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Multiplication is Repeated Addition: |
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m * n = m + m + . . . + m (n times) |
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Thus, Multiplication Distributes Over Addition: |
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a * (b + c) = (a*b) + (a*c) |
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Example: |
2 * (3 + 4) = (2*3) + (2*4) 2*7 = 6 + 8 14 = 14 |
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Exponentiation is Repeated Multiplication: |
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m ^ n = m *m *. . . *m (n times) |
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Thus, Exponentiation Distributes Over Multiplication: |
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(a*b)^n = (a^n)*(b^n) |
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Example: |
(3*4)^2 = (3^2)*(4^2) 12^2 = 9*16 144 = 144 |
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Exponentiation Does NOT Distribute Over Addition!!! |
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(a + b)^n is not equal to (a^n) + (b^n) |
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Example: |
(3 + 4)^2 is not equal to (3^2) + (4^2) 7^2 is not equal to 9 + 16 49 is not equal to 25 |
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This also applies to Square Roots: |
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Example: |
sqrt(9 + 16) is not equal to sqrt(9) + sqrt(16) sqrt(25) is not equal to 3 + 4 5 is not equal to 7 |
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