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Question : 53 of 86

Marks: +1, -0

Value of

2 x^{-\frac{1}{2}} \cdot 3 x^{-1}

x=4

is

$\frac{3}{4}$
4
3.5
4.5

Solution:

Concept:

Simplify the expression using exponent rules, then substitute the value of

x

.

Explanation:

Multiply coefficients:

2 \cdot 3 = 6

.

Add exponents:

x^{-1/2} \cdot x^{-1} = x^{-1/2 + (-1)} = x^{-3/2}

.

So expression becomes

6 x^{-3/2}

.

Substitute

x = 4

:

6 \cdot 4^{-3/2}

.

Evaluate

4^{-3/2} = \frac{1}{4^{3/2}} = \frac{1}{(\sqrt{4})^3} = \frac{1}{2^3} = \frac{1}{8}

.

Then

6 \cdot \frac{1}{8} = \frac{6}{8} = \frac{3}{4}

.

Answer:

\frac{3}{4}

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