Simplify the Expression: 20^6 × 20^2 × 20^4 Using Exponent Rules

Question

Simplify the following equation:

206×202×204= 20^6\times20^2\times20^4=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of powers with an equal base (A)
00:08 equals the same base raised to the sum of the exponents (N+M)
00:12 We will apply this formula to our exercise
00:17 We'll maintain the base and add together the exponents
00:38 This is the solution

Step-by-Step Solution

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

  • Step 1: Identify the given expression 206×202×204 20^6 \times 20^2 \times 20^4 .
  • Step 2: Apply the rule of exponents for multiplication of like bases, which is am×an=am+n a^m \times a^n = a^{m+n} .
  • Step 3: Add the exponents together to simplify the power expression.

Now, let's work through each step:
Step 1: We have 206×202×204 20^6 \times 20^2 \times 20^4 .
Step 2: Apply the property of exponents: 206×202×204=206+2+4 20^6 \times 20^2 \times 20^4 = 20^{6+2+4} .
Step 3: Add the exponents: 6+2+4=12 6 + 2 + 4 = 12 , so the expression simplifies to 2012 20^{12} .

By checking the given choices, the correct one is:

Choice 4: A'+C' are correct

Answer

A'+C' are correct