Question

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

• A. 5
• B. 25
• C. 50
• D. 10

Hint:

When multiplying terms with the same base, add exponents: $a^m \times a^n = a^m+n$.
Also, convert all numbers to the same base for easier simplification.

Answer 1

The Correct Option is A

Step 1: Understand the exponents.
We are given $5^{1/4} \times (125)^{0.25}$. Note that $0.25 = \frac{1}{4}$.
So the expression becomes: \[ 5^{1/4} \times (125)^{1/4} \] Step 2: Express 125 in base 5.
We know $125 = 5^3$. Substituting: \[ 5^{1/4} \times (5^3)^{1/4} \] Step 3: Simplify powers using the law $(a^m)^n = a^{mn$.}
\[ (5^3)^{1/4} = 5^{3/4} \] So our expression becomes: \[ 5^{1/4} \times 5^{3/4} \] Step 4: Add the exponents (since bases are the same).
\[ 5^{1/4 + 3/4} = 5^{4/4} = 5^1 \] Step 5: Final value.
\[ 5^1 = 5 \] \[ \boxed{5} \]