Questions: m^13 / m^5

Solution Steps

To divide powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. This will give you the simplified form of the expression.

To simplify the expression \( \frac{m^{13}}{m^{5}} \), we apply the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). Thus, we have: \[ \frac{m^{13}}{m^{5}} = m^{13-5} = m^{8} \]

Next, we substitute \( m = 2 \) into the simplified expression: \[ m^{8} = 2^{8} \]

Now, we calculate \( 2^{8} \): \[ 2^{8} = 256 \]

Final Answer