Calculate (3×4×5)⁴: Fourth Power of a Triple Product

Question

(3×4×5)4= (3\times4\times5)^4=

Video Solution

Step-by-Step Solution

We use the power law for multiplication within parentheses:

(xy)n=xnyn (x\cdot y)^n=x^n\cdot y^n

We apply it to the problem:

(345)4=344454 (3\cdot4\cdot5)^4=3^4\cdot4^4\cdot5^4

Therefore, the correct answer is option b.

Note:

From the formula of the power property mentioned above, we understand that it refers not only to two terms of the multiplication within parentheses, but also for multiple terms within parentheses.

Answer

34×44×54 3^4\times4^4\times5^4