Simplify the Expression: 5³ × 5⁶ × 5² Using Laws of Exponents

Question

Simplify the following equation:

53×56×52= 5^3\times5^6\times5^2=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of 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'll maintain the base and add up the exponents
00:22 This is the solution

Step-by-Step Solution

To solve the problem of simplifying the expression 53×56×52 5^3 \times 5^6 \times 5^2 , follow these steps:

  • Step 1: Understand that the expression involves multiplying powers with the same base.

  • Step 2: Apply the formula for multiplying powers: am×an=am+n a^m \times a^n = a^{m+n} .

  • Step 3: Combine the exponents by adding them together.

Now, let's work through these steps in detail:
Step 1: Recognize the base is 5, with exponents 3, 6, and 2.
Step 2: Since all terms have the base 5, use the formula for multiplying powers, resulting in a single term where the exponents are added: 53+6+2 5^{3+6+2} .
Step 3: Calculate the sum of the exponents: 3+6+2=11 3 + 6 + 2 = 11 .

Hence, the correct answer is 53+6+2 5^{3+6+2} which simplifies to 511 5^{11} .

Answer

53+6+2 5^{3+6+2}