Final answer:
The expression 5∛6c × 7∛6c simplifies to 35∛36c² by multiplying coefficients and cube roots separately, then combining the results.
Step-by-step explanation:
The expression given is a multiplication of cube root terms: 5∛6c × 7∛6c. To combine these, we can multiply the coefficients (5 and 7) together and also multiply the cube root terms (∛6c and ∛6c) together.
When multiplying coefficients, we simply get the product of the numbers. That is 5 × 7 = 35.
When dealing with the multiplication of cube roots, we use the rule for multiplication of radicals, which states that ∛(a) × ∛(b) = ∛(ab), provided a and b are non-negative.
∛6c × ∛6c is equivalent to ∛(6c × 6c) which simplifies to ∛(36c²).
Therefore, the equivalent expression is 35∛36c².