Simplify 7^6 × 7^6: Exponent Multiplication Practice

Question

Simplify the following equation:

76×76= 7^6\times7^6=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, multiplying exponents with an equal base (A)
00:07 equals the same base raised to the sum of the exponents (N+M)
00:11 We will apply this formula to our exercise
00:14 We will add up the exponents and raise them to this power
00:18 This is the solution

Step-by-Step Solution

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

  • Step 1: Identify the given expression.

  • Step 2: Recognize and apply the exponent multiplication rule.

  • Step 3: Simplify the expression by adding the exponents.

Now, let's work through each step:
Step 1: The expression given is 76×76 7^6 \times 7^6 .
Step 2: Since the bases are the same, apply the exponent rule: am×an=am+n a^m \times a^n = a^{m+n} .
Step 3: By adding the exponents, we have 6+6=12 6 + 6 = 12 .

Therefore, the simplified expression is 76+6 7^{6+6} or 712 7^{12} .

This corresponds to choice 2.

Thus, the solution to the problem is 76+6 7^{6+6} .

Answer

76+6 7^{6+6}