Find the value of 4/(216)-2/3 + 1/(256)-3/4 + 2/(243)-1/5
Solution:
Given, the expression is \(\frac{4}{216^{\frac{-2}{3}}}+\frac{1}{256^{\frac{-3}{4}}}+\frac{2}{243^{\frac{-1}{5}}}\)
We have to find the value of the given expression.
\(\frac{4}{216^{\frac{-2}{3}}}=\frac{4}{(6^{3})^{\frac{-2}{3}}}\)
We know \((a^{m})^{n}=a^{mn}\)
= \(\frac{4}{6^{3\times \frac{-2}{3}}}\)
= \(\frac{4}{6^{-2}}\)
We know 1/a⁻ⁿ = aⁿ
= \(4\times 6^{2}\)
= 4(36)
= 144
\(\frac{1}{256^{\frac{-3}{4}}}=\frac{1}{(4^{4})^{\frac{-3}{4}}}\)
We know \((a^{m})^{n}=a^{mn}\)
= \(\frac{1}{4^{4\times \frac{-3}{4}}}\)
= \(\frac{1}{4^{-3}}\)
We know 1/a⁻ⁿ = aⁿ
= \(1\times 4^{3}\)
= 4(16)
= 64
\(\frac{2}{243^{\frac{-1}{5}}}=\frac{2}{(3^{5})^{\frac{-1}{5}}}\)
We know \((a^{m})^{n}=a^{mn}\)
= \(\frac{2}{3^{5\times \frac{-1}{5}}}\)
= \(\frac{2}{3^{-1}}\)
We know 1/a⁻ⁿ = aⁿ
= \(2\times 3^{1}\)
= 2(3)
= 6
Now, \(\frac{4}{216^{\frac{-2}{3}}}+\frac{1}{256^{\frac{-3}{4}}}+\frac{2}{243^{\frac{-1}{5}}}\) = 144 + 64 + 6
= 144 + 70
= 214
Therefore, the value of the given expression is 214.
✦ Try This: Find the value of \(\frac{2}{27^{\frac{-2}{3}}}+\frac{4}{81^{\frac{-3}{4}}}+\frac{2}{289^{\frac{-1}{2}}}\)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.4 Problem 7
Find the value of 4/(216)-2/3 + 1/(256)-3/4 + 2/(243)-1/5
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 value of the expression is 214
☛ Related Questions:
visual curriculum