Solve (7×4×6×3)⁴: Product of Numbers Raised to Fourth Power

Question

(7⋅4⋅6⋅3)4=? (7\cdot4\cdot6\cdot3)^4= \text{?}

Video Solution

Solution Steps

00:00 Simply
00:03 We'll use the power formula for multiplications
00:06 When we have each multiplication raised to any power (N)
00:09 We can also write this as each factor raised to the exponent (N)
00:13 We'll use this formula in our exercise
00:16 Let's expand the parentheses and raise each factor to its appropriate power
00:19 And this is the solution to the question

Step-by-Step Solution

We use the power property for an exponent that is applied to a set parentheses in which the terms are multiplied:

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

We apply the law in the problem:

(7⋅4⋅6⋅3)4=74⋅44⋅64⋅34 (7\cdot4\cdot6\cdot3)^4=7^4\cdot4^4\cdot6^4\cdot3^4

When we apply the exponent to a parentheses with multiplication, we apply the exponent to each term of the multiplication separately, and we keep the multiplication between them.

Therefore, the correct answer is option a.

Answer

74⋅44⋅64⋅34 7^4\cdot4^4\cdot6^4\cdot3^4

More Questions

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 Power of a Product: Applying the formula Power of a Product: Number of terms