Complete the Expression: (6×7×10) Raised to (y+4+a) Power

Question

Insert the corresponding expression:

(6×7×10)y+4+a= \left(6\times7\times10\right)^{y+4+a}=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:04 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
00:17 Note that our power is actually the sum and the power (N)
00:21 Therefore we will raise each factor to this power
00:37 This is the solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify each factor inside the parentheses: 66, 77, and 1010.
  • Step 2: Use the power of a product rule, (abc)n=an×bn×cn(abc)^n = a^n \times b^n \times c^n, to distribute the exponent y+4+ay + 4 + a to each factor.
  • Step 3: Rewrite the expression with each base raised to the power of y+4+ay + 4 + a.

Now, let's work through each step:
Step 1: We have 6×7×106 \times 7 \times 10 as the base of the expression inside the parentheses.
Step 2: According to the power of a product rule, we distribute y+4+ay + 4 + a across each base, resulting in 6y+4+a×7y+4+a×10y+4+a6^{y+4+a} \times 7^{y+4+a} \times 10^{y+4+a}.
Step 3: Therefore, the expression (6×7×10)y+4+a(6 \times 7 \times 10)^{y+4+a} expands to 6y+4+a×7y+4+a×10y+4+a6^{y+4+a} \times 7^{y+4+a} \times 10^{y+4+a}.

Therefore, the solution to the problem is 6y+4+a×7y+4+a×10y+4+a 6^{y+4+a}\times7^{y+4+a}\times10^{y+4+a} .

Answer

6y+4+a×7y+4+a×10y+4+a 6^{y+4+a}\times7^{y+4+a}\times10^{y+4+a}