Question

The value is? \(5^{\frac{1}{4}}\times(125)^{0.25}\)

• A. 5
• B. 25
• C. 50
• D. 10

Answer 1

The Correct Option is A

To solve the expression \(5^{\frac{1}{4}}\times(125)^{0.25}\), we first need to simplify each term:

\(5^{\frac{1}{4}}\) is evaluating the 4th root of 5.

Similarly, \(125^{0.25}\) means finding the 4th root of 125.

Now, let's simplify \(125^{0.25}\):

Notice that \(125 = 5^3\), so we can rewrite the expression as \((5^3)^{0.25}\).

Using the power of a power property, \((a^m)^n = a^{m \cdot n}\), we have:

\((5^3)^{0.25} = 5^{3 \cdot 0.25} = 5^{0.75}\).

Now our original expression becomes:

\(5^{\frac{1}{4}} \times 5^{0.75}\).

We can now apply the property of exponents \(a^m \times a^n = a^{m+n}\):

\(5^{\frac{1}{4} + 0.75} = 5^{\frac{1}{4} + \frac{3}{4}}\).

Simplifying the exponents: \(\frac{1}{4} + \frac{3}{4} = 1\).

Thus, the expression simplifies to \(5^1 = 5\).

The value is 5.