Simplifying Exponential Expressions

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What is an exponential expression?

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An exponential expression is a mathematical expression in the form of a^b, where 'a' is the base and 'b' is the exponent.

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What does it mean to simplify an exponential expression?

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To simplify an exponential expression means to reduce it to its simplest form, often by applying the laws of exponents.

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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 exponential expressions 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 exponential expressions 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 an exponential expression to another exponent, 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 an exponent, 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 an exponent, you distribute the exponent to the numerator and denominator: (a/b)^n = a^n / b^n.

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

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Using the product of powers property: 2^3 * 2^4 = 2^(3+4) = 2^7.

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How do you simplify the expression 5^6 / 5^2?

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Using the quotient of powers property: 5^6 / 5^2 = 5^(6-2) = 5^4.

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What is the value of (3^2)^3?

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Using the power of a power property: (3^2)^3 = 3^(2*3) = 3^6.