Which power of 8 is equal to `2^(6)`?

Options

A. 3
B. 2
C. 1
D. 4

Answer

To solve the problem of finding which power of 8 is equal to \(2^6\), we can follow these steps:

### Step 1: Set up the equation
We start by assuming that \(8^x = 2^6\). Here, we need to find the value of \(x\).

### Step 2: Rewrite 8 in terms of base 2
Next, we can express 8 as a power of 2. We know that:
\[ 8 = 2^3 \]
So we can rewrite our equation as:
\[ (2^3)^x = 2^6 \]

### Step 3: Apply the power of a power rule
Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\), we can simplify the left side:
\[ 2^{3x} = 2^6 \]

### Step 4: Set the exponents equal to each other
Since the bases are the same (both are base 2), we can set the exponents equal to each other:
\[ 3x = 6 \]

### Step 5: Solve for x
Now, we solve for \(x\) by dividing both sides of the equation by 3:
\[ x = \frac{6}{3} = 2 \]

### Conclusion
Thus, the power of 8 that is equal to \(2^6\) is:
\[ 8^2 \]