Test Index

Indices

© examsnet.com

Question : 37 of 86

Marks: +1, -0

The value of

\sqrt{x^{-1} y} \cdot \sqrt{y^{-1} z} \cdot \sqrt{z^{-1} x}

is:

1
$-1$
0
2.

Solution:

Concept:

Use exponent rules to combine the radicals into a single square root of a product.

Explanation:

Write each square root as a power of

\frac{1}{2}

:

\sqrt{x^{-1} y} \cdot \sqrt{y^{-1} z} \cdot \sqrt{z^{-1} x} = (x^{-1}y)^{\frac{1}{2}} \cdot (y^{-1}z)^{\frac{1}{2}} \cdot (z^{-1}x)^{\frac{1}{2}}

.

Combine the exponents:

(x^{-1}y \cdot y^{-1}z \cdot z^{-1}x)^{\frac{1}{2}}

.

Multiply inside:

x^{-1} \cdot x = 1

,

y \cdot y^{-1} = 1

,

z \cdot z^{-1} = 1

, so product

= 1 \cdot 1 \cdot 1 = 1

.

Thus the expression becomes

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

.

Answer:

1

© examsnet.com

Go to Question:

Prev Question

Next Question