Question

which expression is equivalent to $b^m \cdot b^n$?

a. $b^{m \cdot n}$

b. $b^{m + n}$

c. $b^{m \div n}$

d. $b^{m - n}$

Explanation:

Step1: Recall exponent rule

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

Step2: Apply the rule

For \( b^m \cdot b^n \), using the product rule of exponents, we add the exponents. So \( b^m \cdot b^n = b^{m + n} \).

Answer:

B. \( b^{m + n} \)