Expand the Expression: Calculate 7^8 Step by Step

Question

Expand the following equation:

78= 7^8=

Video Solution

Solution Steps

00:00 Identify the correct solution
00:03 According to the laws of exponents, the multiplication of powers with an equal base (A)
00:07 equals the same base raised to the sum of the exponents (N+M)
00:11 Let's apply the formula and check if this solution is correct
00:16 Upon solving the problem we can observe that the powers are not equal, therefore it's incorrect
00:23 Let's solve the remaining options using the same method
00:30 We can see that this solution is also incorrect
00:38 Let's continue to the last option
00:43 This one also doesn't fit, therefore none of the expressions are correct
00:47 This is the solution

Step-by-Step Solution

To address this problem, we need to verify the set of exponent rules for each choice provided and determine which, if any, results in 78 7^8 .

Let's explore and verify the provided choices:

  • Choice 1: 72×74 7^2 \times 7^4
  • Using the rule am×an=am+n a^m \times a^n = a^{m+n} , we have:

    72×74=72+4=76 7^2 \times 7^4 = 7^{2+4} = 7^6

    This does not equal 78 7^8 .

  • Choice 2: 78×71 7^8 \times 7^1
  • Using the rule am×an=am+n a^m \times a^n = a^{m+n} , we have:

    78×71=78+1=79 7^8 \times 7^1 = 7^{8+1} = 7^9

    This does not equal 78 7^8 .

  • Choice 3: 74×72 7^4 \times 7^2
  • Using the rule am×an=am+n a^m \times a^n = a^{m+n} , we have:

    74×72=74+2=76 7^4 \times 7^2 = 7^{4+2} = 7^6

    This does not equal 78 7^8 .

Upon evaluating all given choices, none of the expressions equal 78 7^8 .

Therefore, based on the analysis, the correct choice is None of the answers are correct.

Answer

None of the answers are correct