Algebra I Recipe: Exponents and Order of Operations |
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A. Definitions
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base – any number, variable, or term raised to an exponent.
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exponent – it tells how many times to multiply the base by itself.
- Given 73, 7 is the base, 3 is the exponent, and it means 7 · 7 · 7.
- Given x5, x is the base, 5 is the exponent, and it means x · x · x · x · x.
- Given (2x)4, 2x is the base, 4 is the exponent, and it means 2x · 2x · 2x · 2x.
- Given 2x4, x is the base, 4 is the exponent, and it means 2 · x · x · x · x.
- Therefore, (2x)4 and 2x4 would not have the same value.
B. Order of Operations
- Do all operations within grouping symbols.
- Evaluate exponents.
- Do multiplication and division from left to right.
- Do addition and subtraction from left to right.
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C. Formulas of a Cube
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Surface Area – the space that covers all sides of the cube where each side or face is exactly the same.
- Find the area of one side or face.
- Multiply that area by 6 since there are 6 identical sides or faces.
- Answer must be in square units such as in2, ft2, cm2.
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Volume – the space inside the cube.
- Multiply the length, width, and height of the cube together. V = l · w · h
- Answer must be in cubic units such as in3, ft3, or cm3
Practice Problems
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G Redden
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