\( \begin{array}{ll}2 & g^{20} \div g^{15} \\ \text { Test if } g\end{array} \)

It looks like you're working with the expression: \[ \frac{g^{20}}{g^{15}} \] To simplify this expression, you can use the **laws of exponents**. Specifically, when you divide two exponents with the same base, you subtract the exponents: \[ \frac{g^{a}}{g^{b}} = g^{a - b} \] Applying this rule to your expression: \[ \frac{g^{20}}{g^{15}} = g^{20 - 15} = g^{5} \] **Simplified Result:** \[ g^5 \] --- **Testing the Simplification:** If you have a specific value for \( g \), you can substitute it into both the original and simplified expressions to verify that they yield the same result. **Example:** Let \( g = 2 \). - Original Expression: \[ \frac{2^{20}}{2^{15}} = \frac{1,048,576}{32,768} = 32 \] - Simplified Expression: \[ 2^{5} = 32 \] Both expressions yield the same result, confirming that the simplification is correct.