Power Rules of Exponents

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What is the Power Rule of Exponents?

Back

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

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How do you simplify the expression 2x^2y^3 (-4xy)^2?

Back

To simplify, first calculate (-4xy)^2 = 16x^2y^2. Then multiply: 2x^2y^3 * 16x^2y^2 = 32x^4y^5.

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What is the product of powers rule?

Back

The Product of Powers Rule 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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How do you simplify the expression (-5a^{-3})(3a^6b)^2?

Back

First, calculate (3a^6b)^2 = 9a^{12}b^2. Then multiply: (-5a^{-3}) * (9a^{12}b^2) = -45a^{9}b^2.

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What is the quotient of powers rule?

Back

The Quotient of Powers Rule 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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How do you simplify the expression 7a^2 (5a^6b)^2?

Back

First, calculate (5a^6b)^2 = 25a^{12}b^2. Then multiply: 7a^2 * 25a^{12}b^2 = 175a^{14}b^2.

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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: a^0 = 1 (where a ≠ 0).

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How do you simplify expressions with negative exponents?

Back

Negative exponents indicate the reciprocal: a^{-n} = 1/a^n.

Front

What is the power of a product rule?

Back

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

Front

What is the power of a quotient rule?

Back

The Power of a Quotient Rule states that when raising a quotient to a power, you apply the exponent to both the numerator and the denominator: (a/b)^n = a^n / b^n.