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

Expand the following equation:

$g^{10a+5x}=$

Video Solution

Solution Steps

00:00 Identify which expressions are equal to the original expression

00:04 According to the laws of exponents, multiplication of exponents with the same base (A)

00:08 equals the same base raised to the sum of the exponents (N+M)

00:11 We will apply this formula to our exercise

00:17 We'll maintain the base and add the exponents together

00:20 We can observe that this expression is not equal to the original expression

00:23 We will use the same method in order to simplify the remaining expressions

00:26 In this expression the operation is addition and not multiplication, therefore it's not relevant

00:39 This expression is equal to the original expression

00:54 This expression is not equal to the original expression

01:00 This is the solution

Step-by-Step Solution

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 $g^{5a+5x} \times g^{5a}$ .