Final answer:
The exponential expression equivalent to (22 * 7)^40 is 22^40 * 7^40. The exponent applies to both the 22 and the 7 when raised to the 40th power.
Step-by-step explanation:
The student's question asks for the equivalent exponential expression of (22 * 7)^40. According to the properties of exponents, when an entire product is raised to a power, the exponent applies to each factor in the product separately. Hence, the expression (22 * 7)^40 is equivalent to 22^40 * 7^40, which is option c. To explain further, if you have a multiplication inside parentheses and the entire term is raised to an exponent, the rule states that you can distribute the exponent to each multiplied factor. This is similar to how you would handle an expression like (2 * 3)^2, which gives you 2^2 * 3^2 = 4 * 9= 36.