PreAlg Ch 4 Powers and Exponents Vocab

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Exponent

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A number that shows how many times the base is multiplied by itself. Example: 3^2 = 3 × 3 = 9. The exponent is 2.

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Power

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The result of multiplying a base by itself as many times as the exponent says. Example: 2^3 = 8.

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Base

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The number that is being multiplied by itself. Example: In 5^3, the base is 5.

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Negative Exponent

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An exponent less than zero. It means you take the reciprocal of the base and make the exponent positive. Example: 2^-3 = 1/2^3 = 1/8.

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Monomial

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An expression that is a single term made up of numbers, variables, or both. Example: 3x^2 or 5.

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Product Rule

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When multiplying two powers with the same base, add their exponents. Example: x^3 · x^2 = x^(3+2) = x^5.

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Power Rule

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When raising a power to another power, multiply the exponents. Example: (x^3)^2 = x^(3 · 2) = x^6.

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Quotient Rule

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When dividing two powers with the same base, subtract the exponents. Example: x^5/x^2 = x^(5-2) = x^3.

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Power of a Product

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To find the power of a product, raise each factor inside the parentheses to the power. Example: (2x)^3 = 2^3 · x^3 = 8x^3.

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Power of a Quotient

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To find the power of a quotient, raise both the numerator and denominator to the power. Example: (x/y)^2 = x^2/y^2.