Simplify 4⁷ × 5³ × 4² × 5⁴: Exponent Multiplication Problem

Video Solution

Solution Steps

00:00 Simply

00:04 We'll use the substitution law and arrange the equal bases together

00:14 We'll use the formula for multiplying powers with powers

00:16 Any number (A) to the power of (M) multiplied by the same number (A) to the power of (N)

00:19 Equals the same number (A) to the power of the sum of exponents (M+N)

00:23 We'll use this formula in our exercise

00:29 And equate the numbers to the variables in the formula

00:40 We'll keep the base and combine the exponents

01:15 We'll use the same method for the second base

01:32 And this is the solution to the question

Step-by-Step Solution

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

Step 1: Identify and group the terms with the same base.
Step 2: Apply the laws of exponents to simplify by adding the exponents of each base.
Step 3: Write the simplified form.

Let's work through each step:

Step 1: We are given that $4^7 \times 5^3 \times 4^2 \times 5^4$ .

Step 2: First, group the terms with the same base:

$4^7 \times 4^2$ and $5^3 \times 5^4$ .

Step 3: Use the law of exponents, which states $a^m \times a^n = a^{m+n}$ .

For the base 4: $4^7 \times 4^2 = 4^{7+2} = 4^9$ .

For the base 5: $5^3 \times 5^4 = 5^{3+4} = 5^7$ .

Therefore, the simplified form of the expression is $4^9 \times 5^7$ .