Simplify 4²×3⁵×4³×3²: Product of Powers Problem

Video Solution

Solution Steps

00:00 Simply

00:04 Let's arrange the exercise so that equal bases are adjacent

00:14 According to the laws of exponents, when multiplying powers with the same base (A)

00:20 We get the same base (A) raised to the sum of the exponents (M+N)

00:23 Let's use this formula in our exercise

00:26 Let's compare terms according to the formula and simplify

00:30 Let's keep the base

00:35 Let's add the exponents

00:57 Let's use the same method to simplify the second base

01:16 And this is the solution to the question

Step-by-Step Solution

To simplify the given expression $4^2 \times 3^5 \times 4^3 \times 3^2$ , we will follow these steps:

Now, let's go through each step thoroughly:

Step 1: Identify and group similar bases:
We see two distinct bases here: 4 and 3.

Step 2: Apply the rule for multiplying like bases:
For base 4: Combine $4^2$ and $4^3$ , using the rule $a^m \times a^n = a^{m+n}$ .

Add the exponents for base 4: $2 + 3 = 5$ , thus, $4^2 \times 4^3 = 4^5$ .

For base 3: Combine $3^5$ and $3^2$ , still using the same exponent rule.

Add the exponents for base 3: $5 + 2 = 7$ , resulting in $3^5 \times 3^2 = 3^7$ .

Step 3: Simplify the expression:
The simplified expression is $4^5 \times 3^7$ .

Therefore, the final simplified expression is $4^5 \times 3^7$ .