Complete the Expression: (7×8) Raised to Power (b+a)

Question

Insert the corresponding expression:

(7×8)b+a= \left(7\times8\right)^{b+a}=

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
00:07 We'll raise each factor to the power (N)
00:11 We apply this formula to our exercise
00:14 Note that the power (N) contains an addition operation
00:18 Therefore we'll raise each factor to this power (N)
00:22 This is the solution

Step-by-Step Solution

To solve this problem, we'll follow the steps below:

First, recognize that the expression given is (7×8)b+a (7 \times 8)^{b+a} . We aim to use the exponent rule known as the power of a product, which states that (xy)n=xn×yn (xy)^n = x^n \times y^n .

Applying this rule to the problem at hand, we have:

(7×8)b+a=7b+a×8b+a (7 \times 8)^{b+a} = 7^{b+a} \times 8^{b+a} .

Thus, the expression is expanded to show each base (7 and 8) raised to the combined power of b+a b+a .

Checking the choices provided, the expanded expression matches option 2.

Therefore, the correct expression is 7b+a×8b+a 7^{b+a}\times8^{b+a} .

Answer

7b+a×8b+a 7^{b+a}\times8^{b+a}