Review Exponents (positive)

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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. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

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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 expressions with the same base, you can add the exponents. For example, 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. For example, (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 can distribute the exponent to each factor. For example, (ab)^n = a^n * b^n.

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What is the zero exponent rule?

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The zero exponent rule states that any non-zero base raised to the power of zero equals one. For example, a^0 = 1, where a ≠ 0.

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What is the negative exponent rule?

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The negative exponent rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, a^(-n) = 1/(a^n), where a ≠ 0.

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How do you simplify the expression 5a^3 * 2a^4?

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To simplify, use the product of powers property: 5a^3 * 2a^4 = (5*2)(a^(3+4)) = 10a^7.

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How do you simplify the expression (3a^2)^4?

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To simplify, use the power of a power property: (3a^2)^4 = 3^4 * (a^2)^4 = 81a^8.

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What is the result of 2^3 * 2^2?

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Using the product of powers property, 2^3 * 2^2 = 2^(3+2) = 2^5 = 32.

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How do you simplify the expression 12b^6 / 3b^2?

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To simplify, use the quotient of powers property: 12b^6 / 3b^2 = (12/3)(b^(6-2)) = 4b^4.