Spring Final Exam Review - Exponent Rules and Exponentials

Front

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).

Front

What is the product of powers rule?

Back

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

Front

What is the power of a power rule?

Back

The power of a power rule states that when raising an exponent to another exponent, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

What is the power of a product rule?

Back

The power of a product rule states that when raising a product to an exponent, 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?

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 negative exponent rule?

Back

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).

Front

Simplify: 3^2 * 3^3

Back

Using the product of powers rule: 3^(2+3) = 3^5 = 243.

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Simplify: (x^4)^2

Back

Using the power of a power rule: x^(4*2) = x^8.

Front

Simplify: (2x^3y^2)^2

Back

Using the power of a product rule: 2^2 * (x^3)^2 * (y^2)^2 = 4x^6y^4.

Front

What is the value of 5^0?

Back

According to the zero exponent rule, 5^0 = 1.