What is the value of x, if `5^(4x)=(625)^6`?

Answer

To solve the equation \(5^{4x} = (625)^6\), we will follow these steps:

### Step 1: Rewrite 625 as a power of 5
First, we need to express 625 in terms of the base 5. We know that:
\[ 625 = 5^4 \]
Thus, we can rewrite the equation:
\[ (625)^6 = (5^4)^6 \]

### Step 2: Apply the power of a power property
Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\), we can simplify \((5^4)^6\):
\[ (5^4)^6 = 5^{4 \cdot 6} = 5^{24} \]

### Step 3: Set the exponents equal to each other
Now we have:
\[ 5^{4x} = 5^{24} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ 4x = 24 \]

### Step 4: Solve for x
To find \(x\), we divide both sides by 4:
\[ x = \frac{24}{4} = 6 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{6} \]

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