Simplify: (1/27)-2/3
Solution:
Given, the expression is \((\frac{1}{27})^{\frac{-2}{3}}\)
We have to simplify the expression.
\((\frac{1}{27})^{\frac{-2}{3}}=(\frac{1}{(3)^{3}})^{\frac{-2}{3}}\)
We know that \((a^{p})^{q}=a^{pq}\)
= \((3^{-3})^{\frac{-2}{3}}\)
= (3)²
= 9
Therefore, \((\frac{1}{27})^{\frac{-2}{3}}\) = 9
✦ Try This: Simplify: \((\frac{1}{64})^{\frac{-2}{3}}\)
Given, the expression is \((\frac{1}{64})^{\frac{-2}{3}}\)
We have to simplify the expression.
\((\frac{1}{64})^{\frac{-2}{3}}=(\frac{1}{(4)^{3}})^{\frac{-2}{3}}\)
= \((4^{-3})^{\frac{-2}{3}}\)
We know that \((a^{p})^{q}=a^{pq}\)
= (4)²
= 16
Therefore, \((\frac{1}{64})^{\frac{-2}{3}}\) = 16
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 14(iii)
Simplify: (1/27)-2/3
Summary:
A number is called a rational number, if it can be written in the form p/q, where p and q are integers and q ≠ 0. The simplified form of (1/27)-⅔ is 9
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