Simplify :\((256)^{-(4)^{\frac{-3}{2}}}\)
Solution:
Given, the expression is \((256)^{-(4)^{\frac{-3}{2}}}\)
We have to simplify the expression.
\((256)^{-(4)^{\frac{-3}{2}}}\)=\(((256)^{-(2^{2})})^{\frac{-3}{2}}\)
= \((256)^{-2^{2\times \frac{-3}{2}}}\)
We know \((b^{a^{m}})^{n}=b^{a^{mn}}\)
= \((256)^{-2^{-3}}\)
We know a⁻ⁿ = 1/aⁿ
= \((256)^{\frac{-1}{2^{3}}}\)
= \((256)^{\frac{-1}{8}}\)
We know \((a^{m})^{n}=a^{mn}\)
= \((2^{8})^{\frac{-1}{8}}\)
= \((2)^{8\times \frac{-1}{8}}\)
= (2)⁻¹
= 1/2
Therefore, \((256)^{-(4)^{\frac{-3}{2}}}\) = 1/2.
✦ Try This: Simplify : \((6561)^{-(4)^{\frac{-3}{2}}}\)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.4 Problem 6
Simplify :\((256)^{-(4)^{\frac{-3}{2}}}\)
Summary:
If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number. The simplified value of the expression is 1/2
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