Exponents Review

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What is an exponent?

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An exponent is a mathematical notation indicating the number of times a number (the base) is multiplied by itself.

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What is the product of powers property?

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The product of powers property states that when multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

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What is the quotient of powers property?

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The quotient of powers property states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

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What is the power of a power property?

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The power of a power property states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

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What is the power of a product property?

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The power of a product property states that when raising a product to a power, you distribute the exponent to each factor: (ab)^n = a^n * b^n.

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What is the power of a quotient property?

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The power of a quotient property states that when raising a quotient to a power, you distribute the exponent to the numerator and denominator: (a/b)^n = a^n / b^n.

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How do you simplify a negative exponent?

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A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/a^n.

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What is the zero exponent rule?

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Any non-zero number raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

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How do you simplify expressions with multiple variables and exponents?

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Combine like terms by applying the product and quotient of powers properties, and simplify each variable separately.

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What is the significance of simplifying expressions in algebra?

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Simplifying expressions makes them easier to work with, helps in solving equations, and clarifies the relationships between variables.