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Definition
For any positive integer n, an = a · a · a · · · a, (number of a's = n factors) where a is the base and n is the exponent. |
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Term
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Definition
For any nonzero real number a, a0 = 1 |
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Term
Negative Exponents in Fractions |
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Definition
For any nonzero numbers a and b, and any integers m and n, a-m/b-n = bn/am. (A factor can be moved to the other side of the fraction bar if the sign of the exponent is changed.) |
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Term
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Definition
For any real numbers a and b and any integers m and n, assuming 0 is not raised to a nonpositive power: am · an = am + n.
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Term
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Definition
For any real numbers a and b and any integers m and n, assuming 0 is not raised to a nonpositive power: am/an = am - n (a ≠ 0).
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Term
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Definition
For any real numbers a and b and any integers m and n, assuming 0 is not raised to a nonpositive power: (am)n = amn.
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Term
Raising a Product to a Power |
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Definition
For any real numbers a and b and any integers m and n, assuming 0 is not raised to a nonpositive power: (ab)m = ambm.
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Term
Raising a Quotient to a Power |
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Definition
For any real numbers a and b and any integers m and n, assuming 0 is not raised to a nonpositive power: (a/b)m = am/bm, (b ≠ 0).
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Term
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Definition
Scientific notation for a number is an expression of the type N X 10m, where 1 ≤ N ≤ 10, N is in decimal notation, and m is an integer.
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Term
Use of Scientific Notation |
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Definition
In scientific notation, positive exponents are used for numbers greater or equal to 10 and negative exponents for numbers between 0 and 1.
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Term
Rules for Order of Operations |
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Definition
- Do all calculations within grouping symbols before operations outside. When nested grouping symboles are present, work from the inside out.
- Evaluate all exponential expressions.
- Do all multiplications and divisions in order from left to right.
- Do all additions and subtractions in order from left to right.
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Term
Negative-Integer Exponents |
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Definition
For any nonzero real number a and any integer m, a-m = 1/am. |
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Term
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Definition
For any real number a, a1 = a. |
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