Expand the Expression: 4^(a+b+c) Using Power Properties

Question

Expand the following equation:

$4^{a+b+c}=$

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

00:03 According to the power laws, the multiplication of powers with equal bases (A)

00:07 equals the same base raised to the sum of the exponents (N+M)

00:10 Let's apply this formula to our exercise

00:15 We can observe that the operation here is addition and not multiplication, therefore it is not relevant

00:20 In this expression there's multiplication between the powers and not addition, it is also not relevant

00:26 We'll maintain the base and add the exponents together

00:36 This is the solution

To solve this problem, we will use the rule of exponents that allows us to expand the sum $a + b + c$ in the exponent:

Given: $4^{a+b+c}$
According to the exponent rule $x^{m+n+p} = x^m \times x^n \times x^p$ , we can express:
Step: Break down $4^{a+b+c}$ to:
$4^a \times 4^b \times 4^c$

Therefore, the expanded form of the equation is $4^a \times 4^b \times 4^c$ .

$4^a\times4^b\times4^c$