Test Index

Indices

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Question : 33 of 86

Marks: +1, -0

Simplified value of

(125)^{\frac{2}{3}} \times \sqrt{25} \times \sqrt[3]{5^{3}} \times 5^{\frac{1}{2}}

3
5
1
none

Solution:

Concept:

Simplify each term using laws of indices, then multiply.

Explanation:

Step 1:

125 = 5^3

, so

(125)^{\frac{2}{3}} = (5^3)^{\frac{2}{3}} = 5^{3 \cdot \frac{2}{3}} = 5^2 = 25

.

Step 2:

\sqrt{25} = 25^{\frac{1}{2}} = (5^2)^{\frac{1}{2}} = 5^{2 \cdot \frac{1}{2}} = 5^1 = 5

.

Step 3:

\sqrt[3]{5^{3}} = (5^3)^{\frac{1}{3}} = 5^{3 \cdot \frac{1}{3}} = 5^1 = 5

.

Step 4: The last term is

5^{\frac{1}{2}} = \sqrt{5}

.

Step 5: Multiply:

25 \times 5 \times 5 \times 5^{\frac{1}{2}} = 25 \times 25 \times 5^{\frac{1}{2}} = 625 \times 5^{\frac{1}{2}} = 625\sqrt{5}

, which is not equal to 3, 5, or 1.

Answer:

None of the given options match; correct option is D.

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