Simplify the Expression: 9^7 × 9^3 × 9^5 Using Exponent Rules

Question

Simplify the following equation:

$9^7\times9^3\times9^5=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:04 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 will apply this formula to our exercise

00:16 We'll maintain the base and add together the exponents

00:23 This is the solution

Step-by-Step Solution

To simplify the expression $9^7 \times 9^3 \times 9^5$ , we will use the multiplication rule for exponents which applies to powers with the same base.

Step 1: Identify that all terms have the same base of 9.
Step 2: Add the exponents together since the bases are the same: $7 + 3 + 5$ .
Step 3: Perform the addition: $7 + 3 + 5 = 15$ .

This results in the expression simplifying to $9^{7+3+5} = 9^{15}$ .

Therefore, the expression $9^7 \times 9^3 \times 9^5$ simplifies to $9^{15}$ .

The correct answer is choice (1): $9^{7+3+5}$ .

Answer

$9^{7+3+5}$

Related Subjects

Multiplying Exponents with the Same Base

Question Types

Multiplication of Powers: Number of terms Multiplication of Powers: System of equations with no solution