Complete the Expression: Finding (5×b×a)⁴

Question

Insert the corresponding expression:

(5×b×a)4= \left(5\times b\times a\right)^4=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 In order to open parentheses with a multiplication operation and an outside exponent
00:08 Raise each factor to the power
00:14 We will apply this formula to our exercise
00:26 This is the solution

Step-by-Step Solution

To solve the expression (5×b×a)4 \left(5 \times b \times a\right)^4 , we'll apply the Power of a Product Rule, which states that when a product is raised to an exponent, each factor in the product is raised to that exponent individually.

  • First, identify each factor in the product: 5 5 , b b , and a a .

  • Next, apply the exponent to each factor:

    • The number 5 5 becomes 54 5^4 .

    • The variable b b becomes b4 b^4 .

    • The variable a a becomes a4 a^4 .

  • Finally, multiply these results together to obtain the simplified expression.

Therefore, the expression (5×b×a)4 \left(5 \times b \times a\right)^4 simplifies to 54×b4×a4 5^4 \times b^4 \times a^4 , which corresponds to Choice 3.

Answer

54×b4×a4 5^4\times b^4\times a^4