Question

quiz 1: lessons 1.1 and 1.2 question 3 · 1 point simplify: $4^{x} cdot 4^{15} cdot 4^{7}$. provide your answer below: $4^{x + 22}$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying exponential expressions with the same base, we use the rule \(a^m \cdot a^n = a^{m + n}\). Here, the base \(a = 4\), and we have three terms: \(4^z\), \(4^{15}\), and \(4^7\).

Step2: Apply the exponent rule

First, multiply \(4^z\) and \(4^{15}\): \(4^z \cdot 4^{15}=4^{z + 15}\). Then, multiply the result by \(4^7\): \(4^{z + 15}\cdot 4^7 = 4^{(z + 15)+7}\).

Step3: Simplify the exponent

Simplify the exponent \((z + 15)+7\) to \(z + 22\). So the simplified form is \(4^{z + 22}\).

Answer:

\(4^{z + 22}\)