The value of `5^{1 / 4} \times(125)^{0.25}` is:

Options

A. `\sqrt{5}`
B. 5`\sqrt{5}`
C. 5
D. 25

Answer

To solve the expression \(5^{1/4} \times (125)^{0.25}\), we can follow these steps:

### Step 1: Rewrite the base of the second term
We know that \(125\) can be expressed as a power of \(5\):
\[ 125 = 5^3 \]
Thus, we can rewrite \((125)^{0.25}\) as:
\[ (125)^{0.25} = (5^3)^{0.25} \]

### Step 2: Apply the power of a power property
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify:
\[ (5^3)^{0.25} = 5^{3 \cdot 0.25} = 5^{3/4} \]

### Step 3: Combine the terms
Now we can substitute back into the original expression:
\[ 5^{1/4} \times 5^{3/4} \]
Using the property of exponents that states \(a^m \times a^n = a^{m+n}\), we combine the exponents:
\[ 5^{1/4 + 3/4} = 5^{4/4} \]

### Step 4: Simplify the exponent
Since \(4/4 = 1\), we have:
\[ 5^{4/4} = 5^1 = 5 \]

### Final Answer
Thus, the value of \(5^{1/4} \times (125)^{0.25}\) is:
\[ \boxed{5} \]

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