Properties of Exponents

Front

What is the Quotient Rule for exponents?

Back

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

Front

What is the value of any non-zero number raised to the power of 0?

Back

Any non-zero number raised to the power of 0 is equal to 1: \( a^0 = 1 \) for \( a \neq 0 \).

Front

What is the Product Rule for exponents?

Back

The Product Rule states that when multiplying two powers with the same base, you add the exponents: \( a^m \cdot a^n = a^{m+n} \).

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Back

Using the Product Rule: \( x^{10} \cdot x^{5} = x^{10+5} = x^{15} \).

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Back

Using the Quotient Rule: \( \frac{x^{8}}{x^{3}} = x^{8-3} = x^{5} \).

Front

What is the Power of a Power Rule?

Back

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

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Back

Using the Power of a Power Rule: \( (x^{2})^{3} = x^{2 \cdot 3} = x^{6} \).

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Back

The value is -8, since \( (-2) \cdot (-2) \cdot (-2) = -8 \).

Front

What does it mean to have a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent: \( a^{-n} = \frac{1}{a^{n}} \).

Front

Back

Using the definition of negative exponents: \( x^{-4} = \frac{1}{x^{4}} \).