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Question : 68 of 86

Marks: +1, -0

The value of

5^{\frac{1}{4}} \times (125)^{0.25}

is

$\sqrt{5}$
5
$\sqrt[3]{5}$
25

Solution:

Concept:

Simplify by expressing all terms with the same base and using the law of indices

a^m \times a^n = a^{m+n}

.

Explanation:

5^{\frac{1}{4}} \times (125)^{0.25}

Rewrite

125

as

5^3

:

5^{\frac{1}{4}} \times (5^3)^{0.25}

Using

(a^m)^n = a^{mn}

:

5^{\frac{1}{4}} \times 5^{3 \times 0.25} = 5^{\frac{1}{4}} \times 5^{0.75}

0.75 = \frac{3}{4}

, so we have

5^{\frac{1}{4}} \times 5^{\frac{3}{4}}

Using

a^m \times a^n = a^{m+n}

:

5^{\frac{1}{4} + \frac{3}{4}} = 5^{1} = 5

Answer:

5

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