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# Assuming that X, Y, Z Are Positive Real Numbers, Simplify the Following: (X^((-2)/3)Y^((-1)/2))^2 - CBSE Class 9 - Mathematics

ConceptLaws of Exponents for Real Numbers

#### Question

Assuming that x, y, z are positive real numbers, simplify the following:

(x^((-2)/3)y^((-1)/2))^2

#### Solution

We have to simplify the following, assuming that x, y, z are positive real numbers

Given (x^((-2)/3)y^((-1)/2))^2

As x and y are positive real numbers then we have

(x^((-2)/3)y^((-1)/2))^2=(x^((-2)/3)xxx^((-2)/3)xxy^((-1)/2)xxy^((-1)/2))

By using law of rational exponents a^-n=1/a^n we have

(x^((-2)/3)y^((-1)/2))^2=1/x^(2/3)xx1/x^(2/3)xx1/y^(1/2)xx1/y^(1/2)

(x^((-2)/3)y^((-1)/2))^2=1/(x^(2/3)xx x^(2/3))xx1/(y^(1/2)xxy^(1/2))

By using law of rational exponents a^m xx a^n=a^(m+n) we have

(x^((-2)/3)y^((-1)/2))^2=1/x^(2/3+2/3)xx1/y^(1/2+1/2)

=1/x^(4/3)xx1/y^(2/2)

=1/x^(4/3)xx1/y

=1/(x^(4/3)y)

Hence the simplified value of (x^((-2)/3)y^((-1)/2))^2 is 1/(x^(4/3)y)

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#### APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.20 | Q: 1.3 | Page no. 24

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Solution Assuming that X, Y, Z Are Positive Real Numbers, Simplify the Following: (X^((-2)/3)Y^((-1)/2))^2 Concept: Laws of Exponents for Real Numbers.
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