Solve the following equations.
`x^(3)=64`

Answer

To solve the equation \( x^3 = 64 \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ x^3 = 64 \]

### Step 2: Factorize 64
Next, we need to express 64 as a power of a number. We can factor 64:
\[ 64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^6 \]

### Step 3: Express 64 as a cube
We can also express 64 in terms of a cube:
\[ 64 = 4^3 \]
This is because \( 4 = 2^2 \), so \( 4^3 = (2^2)^3 = 2^{2 \times 3} = 2^6 \).

### Step 4: Set the cubes equal
Now we can rewrite our original equation using this expression:
\[ x^3 = 4^3 \]

### Step 5: Compare the bases
Since the bases are the same, we can set the exponents equal to each other:
\[ x = 4 \]

### Step 6: Conclusion
Thus, the solution to the equation \( x^3 = 64 \) is:
\[ \boxed{4} \]

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