Question

simplify $2^3 \cdot 2^7$.\
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a. $2^{-4}$\
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b. $2^{21}$\
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c. $2^9$\
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d. $2^{10}$

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we use the rule \(a^m \cdot a^n = a^{m + n}\). Here, \(a = 2\), \(m = 3\), and \(n = 7\).

Step2: Apply the rule

Substitute the values into the rule: \(2^3 \cdot 2^7 = 2^{3 + 7}\).

Step3: Calculate the exponent

Add the exponents: \(3 + 7 = 10\), so \(2^3 \cdot 2^7 = 2^{10}\).

Answer:

D. \(2^{10}\)