Exponent Rules FLASHCARD

The Quotient Rule states that when dividing two powers with the same base, you subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \).

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

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

The Power of a Quotient Rule states that when raising a quotient to a power, you distribute the exponent to the numerator and denominator: \( \left( \frac{a}{b} \right)^n = \frac{a^n}{b^n} \).

The Zero Exponent Rule states that any non-zero base raised to the power of zero equals one: \( a^0 = 1 \) (where \( a \neq 0 \)).

The value of \((-4)^2\) is 16.

Any expression (except zero) raised to the power of zero equals one: \( a^0 = 1 \) (where \( a \neq 0 \)).

To simplify \( \frac{x^{12}}{x^2} \), use the Quotient Rule: \( x^{12-2} = x^{10} \).

The result of \( (5x^5)^2 \) is \( 25x^{10} \) using the Power of a Product Rule.

To simplify \( \frac{10x^{15}}{2x^3} \), divide the coefficients and subtract the exponents: \( \frac{10}{2} = 5 \) and \( x^{15-3} = x^{12} \), resulting in \( 5x^{12} \).