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:

(x⋅y)n=xn⋅yn (x\cdot y)^n=x^n\cdot y^n

We apply it to the problem:

(3⋅4⋅5)4=34⋅44⋅54 (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

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Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Exponent of a Multiplication

Question Types

Applying Combined Exponents Rules: Applying the formula Applying Combined Exponents Rules: Number of terms Applying Combined Exponents Rules: A power law Applying Combined Exponents Rules: Trinomial Power of a Product: Applying the formula Power of a Product: Number of terms