Question

Find the equivalent expression using the same bases ((41 cdot 31)^2).

a. (41^2 cdot 31^2)
b. (41^2 + 31^2)
c. (41^2 div 31^2)
d. (41^2 cdot 31)

Answer 1

The equivalent expression using the same bases for ((41 × 31)^2) is (41^2 × 31^2).

Step-by-step explanation:

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

The equivalent expression using the same bases for ((41 × 31)^2) is option a. (41^2 × 31^2).

When we have an expression with the same bases raised to a power, we can distribute the power to each factor inside the parentheses. In this case, (41 × 31)^2 can be written as 41^2 × 31^2.

Therefore, option a. (41^2 × 31^2) is the correct equivalent expression.