Simplify: 64-1/3[641/3 - 642/3]
Solution:
Given, the expression is \((64)^{\frac{-1}{3}}[(64)^{\frac{1}{3}}-(64)^{\frac{2}{3}}]\)
We have to simplify the expression.
\((64)^{\frac{1}{3}}=(4^{3})^{\frac{1}{3}}\)
We know \((a^{m})^{n}=a^{mn}\)
=\((4)^{3\times \frac{1}{3}}\)
= 4
\((64)^{\frac{2}{3}}=(4^{3})^{\frac{2}{3}}\)
We know \((a^{m})^{n}=a^{mn}\)
=\((4)^{3\times \frac{2}{3}}\)
= (4)²
= 16
\([(64)^{\frac{1}{3}}-(64)^{\frac{2}{3}}]\) = (4 - 16)
= -12
\((64)^{\frac{-1}{3}}=(4^{3})^{\frac{-1}{3}}\)
We know \((a^{m})^{n}=a^{mn}\)
=\((4)^{3\times \frac{-1}{3}}\)
= (4)⁻¹
= 1/4
\((64)^{\frac{-1}{3}}[(64)^{\frac{1}{3}}-(64)^{\frac{2}{3}}]\) = (1/4)(-12)
= -12/4
= -3
Therefore, the simplified value is -3
✦ Try This: simplify : \((32)^{\frac{-1}{3}}[(32)^{\frac{1}{3}}-(32)^{\frac{2}{3}}]\)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 14(vi)
Simplify: 64-1/3[641/3 - 642/3]
Summary:
Rational numbers can be added, subtracted, multiplied, or divided just like fractions. The simplified form of the expression 64-1/3[641/3 - 642/3] is -3
☛ Related Questions:
visual curriculum