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

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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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