Simplify the Expression: 6^a × 6^4a Using Laws of Exponents

Question

Reduce the following equation:

6a×64a= 6^a\times6^{4a}=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of powers with equal bases (A)
00:06 equals the same base raised to the sum of the exponents (N+M)
00:10 We will apply this formula to our exercise
00:15 We'll maintain the base and add the exponents together
00:21 This is the solution

Step-by-Step Solution

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

  • Identify the given expression and its components.

  • Recognize that both terms share the same base.

  • Apply the rule for multiplying powers with the same base, bm×bn=bm+nb^m \times b^n = b^{m+n}.

  • Calculate the exponent by adding the powers together.

Let's work through these steps:

Given the expression:
6a×64a 6^a \times 6^{4a}

Since both terms share the same base (6), we use the rule for multiplying powers with the same base:

6a×64a=6a+4a 6^a \times 6^{4a} = 6^{a + 4a} .

Simplify the exponent:

a+4a=5a a + 4a = 5a .

Thus, the expression simplifies to:

65a 6^{5a} .

Since the correct placement of our steps has directly given us choice C and corroborated choice B as intermediary work, B+C represents the comprehensive workings of the problem; thus, B+C are correct is the most comprehensive solution.

Answer

B+C are correct