Solve (y×7×3)⁴: Finding the Fourth Power of a Product

Question

(y×7×3)4= (y\times7\times3)^4=

Video Solution

Solution Steps

00:09 Let's start by breaking it down.
00:12 We're using the power of products rule.
00:15 If a product is raised to a power, say N.
00:19 Each part of the product is raised to the same power N.
00:29 Now, let's apply this rule to solve our problem.
00:33 Open the parentheses. Raise each factor to the correct power.
00:38 And that's how we find the 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 in the problem:

(y⋅7⋅3)4=y4⋅74⋅34 (y\cdot7\cdot3)^4=y^4\cdot7^4\cdot3^4

Therefore, the correct answer is option a.

Note:

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

Answer

y4×74×34 y^4\times7^4\times3^4

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: A power law Applying Combined Exponents Rules: Single Variable Applying Combined Exponents Rules: Binomial Applying Combined Exponents Rules: Variable in the base of the power Power of a Product: Variable in the base of the power