Final Review Practice: Exponents and Natural Base e

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What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base 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 does it mean to simplify an expression with exponents?

Back

Simplifying an expression with exponents means to rewrite it in a simpler form, often by combining like terms and ensuring all exponents are positive.

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What is the product of powers property?

Back

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

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What is the quotient of powers property?

Back

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

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What is the power of a power property?

Back

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 zero exponent rule?

Back

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 natural base e?

Back

The natural base e is an irrational number approximately equal to 2.71828, and it is the base of the natural logarithm. It is used in exponential growth and decay models.

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How do you express exponential growth?

Back

Exponential growth can be expressed with the function y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

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How do you express exponential decay?

Back

Exponential decay can be expressed with the function y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

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What is the difference between exponential growth and decay?

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Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.