Simplify the Expression: 3^4 × 3^5 Using Laws of Exponents

Question

Simplify the following equation:

34×35= 3^4\times3^5=

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 is equal to the same base raised to the sum of the exponents (N+M)
00:11 We'll apply this formula to our exercise
00:14 We'll add up the exponents and then 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 and its components.

  • Step 2: Apply the exponent multiplication formula.

  • Step 3: Simplify the result.

Now, let's work through each step:
Step 1: The given expression is 34×35 3^4 \times 3^5 . We recognize that the base is 3 and the exponents are 4 and 5.
Step 2: Apply the rule for multiplying powers with the same base: am×an=am+n a^m \times a^n = a^{m+n} . Using this formula, we add the exponents: 4+5 4 + 5 .
Step 3: Simplify the expression: 34+5=39 3^{4+5} = 3^9 .

Therefore, the simplified form of the expression is 34+5 3^{4+5} .

Answer

34+5 3^{4+5}