Question

1
simplify $8^5 \cdot 8^4$.
a. $64^9$
b. $8^{20}$
c. $16^9$
d. $8^9$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two exponential expressions with the same base, we use the rule \(a^m \cdot a^n = a^{m + n}\), where \(a\) is the base and \(m\), \(n\) are exponents. Here, the base \(a = 8\), \(m = 5\), and \(n = 4\).

Step2: Apply the rule

Substitute the values into the rule: \(8^5 \cdot 8^4 = 8^{5 + 4}\).

Step3: Calculate the exponent

Add the exponents: \(5 + 4 = 9\), so \(8^5 \cdot 8^4 = 8^9\).

Answer:

D. \(8^9\)