Question

8·8^{a+3}·8^{3a} =

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we add the exponents: \(x^m \cdot x^n = x^{m + n}\). Also, note that \(8 = 8^1\).
So, rewrite the expression \(8 \cdot 8^{a + 3} \cdot 8^{3a}\) as \(8^1 \cdot 8^{a + 3} \cdot 8^{3a}\).

Step2: Apply the exponent rule

Now, add the exponents: \(1+(a + 3)+3a\).
First, simplify the exponent: \(1+a + 3+3a=4 + 4a\).
So the expression becomes \(8^{4 + 4a}\). We can also factor out 4 from the exponent: \(8^{4(1 + a)}\) or leave it as \(8^{4a + 4}\).

Answer:

\(8^{4a + 4}\) (or \(8^{4(1 + a)}\))