Simplify : (3/5)4 (8/5)-12 (32/5)6
Solution:
Given, the expression is \((\frac{3}{5})^{4}\times (\frac{8}{5})^{-12}\times (\frac{32}{5})^{6}\)
We have to simplify the expression.
\((\frac{3}{5})^{4}=\frac{3^{4}}{5^{4}}\)
\((\frac{8}{5})^{-12}=(\frac{5}{8})^{12}=\frac{5^{12}}{8^{12}}= (\frac{5^{12}}{(2^{3})^{12}})=(\frac{5^{12}}{2^{36}})\)
\((\frac{32}{5})^{6}=\frac{32^{6}}{5^{6}}=\frac{(2^{5})^{6}}{5^{6}}=\frac{2^{30}}{5^{6}}\)
= \((\frac{3}{5})^{4}\times (\frac{8}{5})^{-12}\times (\frac{32}{5})^{6}=\frac{3^{4}}{5^{4}}\times (\frac{5^{12}}{2^{36}})\times (\frac{2^{30}}{5^{6}})=3^{4}\times 5^{(12-4-6)}\times (\frac{1}{2^{(36-30)}})=3^{4}\times 5^{2}\times (\frac{1}{2^{6}})\)
3⁴ = 81
5² = 25
2⁶ = 64
So, (3⁴×5²)/2⁶ = (81×25)/64
= 2025/64
Therefore, the simplified value is 2025/64
✦ Try This: Simplify: \((\frac{4}{3})^{4}\times (\frac{36}{5})^{-14}\times (\frac{8}{5})^{6}\)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 14(ii)
Simplify : (3/5)4 (8/5)-12 (32/5)6
Summary:
All rational numbers and all irrational numbers together make the collection of real numbers. The simplified value of the expression (3/5)4 (8/5)-12 (32/5)6 is 2025/64
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