Simplified value of `(25)^(1//3) xx 5^(1//3)` is

Options

A. `25`
B. `3`
C. `1`
D. `5`

Answer

To simplify the expression \((25)^{1/3} \times (5)^{1/3}\), we can follow these steps:

### Step 1: Rewrite 25 as a power of 5
We know that \(25\) can be expressed as \(5^2\). Therefore, we can rewrite the expression as:
\[ (25)^{1/3} = (5^2)^{1/3} \]

### Step 2: Apply the power of a power rule
Using the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\), we can simplify:
\[ (5^2)^{1/3} = 5^{2 \cdot (1/3)} = 5^{2/3} \]

### Step 3: Combine the two terms
Now we can substitute back into the original expression:
\[ (25)^{1/3} \times (5)^{1/3} = 5^{2/3} \times 5^{1/3} \]

### Step 4: Use the product of powers rule
According to the product of powers rule, which states that \(a^m \times a^n = a^{m+n}\), we can combine the exponents:
\[ 5^{2/3} \times 5^{1/3} = 5^{(2/3) + (1/3)} \]

### Step 5: Add the exponents
Now, we add the exponents:
\[ (2/3) + (1/3) = 3/3 = 1 \]

### Step 6: Simplify the expression
Thus, we have:
\[ 5^{3/3} = 5^1 = 5 \]

### Final Answer
The simplified value of \((25)^{1/3} \times (5)^{1/3}\) is:
\[ \boxed{5} \]

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