Solve (9²)⁴: Evaluating Nested Power Expressions

Insert the corresponding expression:

$\left(9^2\right)^4=$

Video Solution

Solution Steps

00:00 Simply

00:02 We'll use the power of a power formula

00:04 Any number (A) to the power of (M) to the power of (N)

00:07 Equals the same number (A) to the power of the product of exponents (M*N)

00:10 We'll use this formula in our exercise

00:13 And we'll equate the numbers with the variables in the formula

00:30 We'll keep the base and multiply the exponents

00:41 Let's calculate the product

00:44 And this is the solution to the question

Step-by-Step Solution

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

Now, let's work through each step:

Step 1: We have the expression $(9^2)^4$ .

Step 2: Using the power of a power rule ( $(a^m)^n = a^{m \cdot n}$ ), apply it to the expression:

$(9^2)^4 = 9^{2 \times 4}$

Step 3: Simplify by calculating the product of the exponents:

$2 \times 4 = 8$

Therefore, $(9^2)^4 = 9^8$ .

The correct expression corresponding to the given problem is $\boxed{9^8}$ .