Quotient of Powers

Front

What is the Quotient of Powers rule in exponents?

Back

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

Front

How do you simplify \( \frac{x^5}{x^{-1}} \)?

Back

Using the Quotient of Powers rule, \( \frac{x^5}{x^{-1}} = x^{5 - (-1)} = x^{5 + 1} = x^6 \).

Front

What is the result of \( \frac{6^7}{6^2} \)?

Back

Using the Quotient of Powers rule, \( \frac{6^7}{6^2} = 6^{7-2} = 6^5 \).

Front

How do you simplify \( \frac{4^{11}}{4^5} \)?

Back

Using the Quotient of Powers rule, \( \frac{4^{11}}{4^5} = 4^{11-5} = 4^6 \).

Front

What is the value of \( \frac{5^6}{5^1} \)?

Back

Using the Quotient of Powers rule, \( \frac{5^6}{5^1} = 5^{6-1} = 5^5 \).

Front

What is the result of \( \frac{10^2}{10^2} \)?

Back

Using the Quotient of Powers rule, \( \frac{10^2}{10^2} = 10^{2-2} = 10^0 = 1 \).

Front

What happens when you divide a number by itself in terms of exponents?

Back

When you divide a number by itself, the result is 1, which corresponds to the exponent rule that states \( a^n / a^n = a^{n-n} = a^0 = 1 \).

Front

What is the significance of negative exponents in the Quotient of Powers rule?

Back

Negative exponents indicate the reciprocal of the base raised to the positive exponent: \( a^{-n} = \frac{1}{a^n} \).

Front

How can you express \( \frac{a^m}{a^n} \) when m < n?

Back

When \( m < n \), the result will be a fraction: \( \frac{a^m}{a^n} = \frac{1}{a^{n-m}} \).

Front

What is the general formula for the Quotient of Powers rule?

Back

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