Simplify the Expression: 5^2 × 5^a × 5^3 Using Exponent Rules

Question

52×5a×53= 5^2\times5^a\times5^3=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of exponents with equal bases (A)
00:07 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
00:38 This is the solution

Step-by-Step Solution

To solve the expression 52×5a×535^2 \times 5^a \times 5^3, we will make use of the exponent rule for multiplication, which states that if you multiply powers with the same base, you add the exponents:

am×an=am+n a^m \times a^n = a^{m+n}

Let's apply this rule step by step:

  • Step 1: Identify the base of the power terms. In this problem, the base is 55.
  • Step 2: Write down all the exponents. The exponents we have are 22, aa, and 33.
  • Step 3: Add the exponents together:
    2+a+32 + a + 3.
  • Step 4: Simplify the sum: 2+a+3=5+a2 + a + 3 = 5 + a.
  • Step 5: Express the final result as a single power:
    The expression can be rewritten using the exponent rule as 55+a5^{5+a}.

Thus, the final simplified expression is 55+a 5^{5+a} .

Answer

55+a 5^{5+a}