Simplify : [[(625)-½]-¼]2
Solution:
Given, the expression is \((((625)^{\frac{-1}{2}})^{\frac{-1}{4}})^{2}\)
We have to simplify the expression.
We know that \((a^{p})^{q}=a^{pq}\)
\((((625)^{\frac{-1}{2}})^{\frac{-1}{4}})^{2}=((625)^{\frac{-1}{2}})^{\frac{-2}{4}}\)
= \((625)^{\frac{-1}{2}})^{\frac{-1}{2}}\)
= \((625)^{\frac{1}{4}})\)
= \((5^{4})^{\frac{1}{4}})\)
= 5
Therefore, \((((625)^{\frac{-1}{2}})^{\frac{-1}{4}})^{2}\) = 5
✦ Try This: Simplify: \(((16)^{\frac{-1}{2}})^{\frac{-1}{4}})^{2}\)
Given, the expression is \(((16)^{\frac{-1}{2}})^{\frac{-1}{4}})^{2}\)
We have to simplify the expression.
We know that \((a^{p})^{q}=a^{pq}\)
\((((16)^{\frac{-1}{2}})^{\frac{-1}{4}})^{2}=((625)^{\frac{-1}{2}})^{\frac{-2}{4}}\)
= \((16)^{\frac{-1}{2}})^{\frac{-1}{2}}\)
= \((16)^{\frac{1}{4}})\)
= \((2^{4})^{\frac{1}{4}})\)
= 2
Therefore, \((((16)^{\frac{-1}{2}})^{\frac{-1}{4}})^{2}\) = 2
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 14(iv)
Simplify : [[(625)-½]-¼]2
Summary:
A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The simplified form of [[(625)-½]-¼]2 is 5
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