Contemporary Math Dividing Exponents

Front

What is the rule for dividing exponents with the same base?

Back

When dividing exponents with the same base, subtract the exponent of the denominator from the exponent of the numerator: \( a^m \div a^n = a^{m-n} \).

Front

Simplify the expression: \( \frac{x^{12} \cdot y^5}{x^7 \cdot y^2} \).

Back

The simplified expression is \( x^5 \cdot y^3 \).

Front

Evaluate the expression: \( \frac{(5^8 \cdot 6^5)}{(5^4 \cdot 6^3)} \).

Back

The evaluated expression is \( 5^4 \cdot 6^2 \).

Front

What is the result of \( \frac{p^{30} \cdot q^{20}}{p^{15} \cdot q^{10}} \)?

Back

The result is \( p^{15} \cdot q^{10} \).

Front

Evaluate the expression: \( \frac{(3^4 \cdot 2^3)}{(3^2 \cdot 2^2)} \).

Back

The evaluated expression is \( 3^2 \cdot 2 \).

Front

What is the general formula for simplifying a fraction with exponents?

Back

The general formula is: \( \frac{a^m}{a^n} = a^{m-n} \).

Front

How do you handle coefficients when dividing expressions with exponents?

Back

Divide the coefficients separately from the variables, applying the exponent rules to each variable.

Front

What happens when you divide a base raised to a power by itself?

Back

When you divide a base raised to a power by itself, the result is 1: \( \frac{a^n}{a^n} = 1 \).

Front

What is the result of dividing a variable with a higher exponent by the same variable with a lower exponent?

Back

The result is the variable raised to the difference of the exponents: \( \frac{x^m}{x^n} = x^{m-n} \) if \( m > n \).

Front

What is the significance of the exponent zero?

Back

Any non-zero base raised to the exponent zero equals 1: \( a^0 = 1 \) for \( a \neq 0 \).