Expand the Expression: Breaking Down g^(10a+5x)

To solve this problem, we will use the properties of exponents:

• Step 1: Recognize that the exponent $10a + 5x$ can be expressed as the sum of two terms, namely $(5a + 5x) + 5a$.
• Step 2: Apply the property $g^{m+n} = g^{m} \times g^{n}$ to the expression $g^{10a + 5x}$.
• Step 3: Expand the expression using the identified split:
  Since $10a + 5x = (5a + 5x) + 5a$, we have:
  $g^{10a + 5x} = g^{(5a + 5x) + 5a} = g^{5a + 5x} \times g^{5a}$.

Thus, the expanded form of the expression is given by $g^{5a+5x} \times g^{5a}$.