$$ \begin{array}{ll}2 & g^{20} \div g^{15} \ ext { Test if } g\end{array} $$

Question

$$ \begin{array}{ll}2 & g^{20} \div g^{15} \ 	ext { Test if } g\end{array} $$

UpStudy AI · Accepted Answer

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.
$$ g^5 $$

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