Question

simplify $4^{3} \cdot 4^{5}$.\
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a. $4^{8}$\
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b. $16 \cdot 15$\
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c. $4^{15}$\
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d. $16^{8}$

Explanation:

Step1: Recall the 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 \(m\) and \(n\) are the exponents.

Step2: Apply the rule to \(4^3 \cdot 4^5\)

Here, the base \(a = 4\), \(m = 3\), and \(n = 5\). So we add the exponents: \(4^{3 + 5}\).

Step3: Calculate the sum of the exponents

\(3+5 = 8\), so \(4^3 \cdot 4^5=4^8\).

Answer:

A. \(4^8\)