Classwork: 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 Zero Exponent Rule?

Back

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

Front

What is the Power Rule for exponents?

Back

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

Front

Simplify using the Quotient Rule: \( \frac{2x^{14}}{x^2} \)

Back

\( 2x^{12} \) (subtract the exponents: 14 - 2 = 12).

Front

Simplify using the Zero Rule: \( -4x^0 \)

Back

-4 (since \( x^0 = 1 \)).

Front

Simplify using the Power Rule: \( (5^3x^2y^4)^0 \)

Back

1 (any expression raised to the power of zero equals one).

Front

Use the Quotient Rule to simplify: \( \frac{12x^9y^4z^2}{24x^3y^4z^6} \)

Back

\( \frac{x^6}{2z^4} \) (divide coefficients and subtract exponents).

Front

Use the Quotient Rule: \( \frac{x^{-7}}{x^4} \)

Back

\( \frac{1}{x^{11}} \) (subtract the exponents: -7 - 4 = -11).

Front

What happens when you multiply two powers with the same base?

Back

You add the exponents: \( a^m \cdot a^n = a^{m+n} \).

Front

What is the definition of a negative exponent?

Back

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