Laws of Exponents: Dividing by the Same Base

Front

What is the Quotient Rule for Exponents?

Back

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

Front

Evaluate: \( y^{15} \div y^{10} \)

Back

\( y^{5} \) (using the Quotient Rule: 15 - 10 = 5).

Front

Evaluate: \( 9^{9} \div 9^{4} \)

Back

\( 9^{5} \) (using the Quotient Rule: 9 - 4 = 5).

Front

Evaluate: \( 3^{4} \div 3^{4} \)

Back

\( 3^{0} = 1 \) (any number to the power of 0 is 1).

Front

Evaluate: \( 15^{9} \div 15^{3} \)

Back

\( 15^{6} \) (using the Quotient Rule: 9 - 3 = 6).

Front

Evaluate: \( \frac{18w^{15}v^{10}}{6w^{3}v^{2}} \)

Back

\( 3w^{12}v^{8} \) (divide coefficients and apply the Quotient Rule to the variables).

Front

What happens when you divide a number by itself?

Back

The result is 1 (e.g., \( a \div a = 1 \) for any non-zero number a).

Front

If \( a^{m} \div a^{n} = a^{x} \), what is x?

Back

\( x = m - n \) (according to the Quotient Rule).

Front

Evaluate: \( 2^{10} \div 2^{7} \)

Back

\( 2^{3} \) (using the Quotient Rule: 10 - 7 = 3).

Front

Evaluate: \( 5^{8} \div 5^{5} \)

Back

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