Question

Evaluate the following:

(4^-3×6^-3÷2^-3)^-1​

Answer 1

$\huge\tt\blue {Question }$

${( {4}^{ - 3} \times {6}^{ - 3} \div {2}^{ - 3} )}^{ - 1}$

$\huge\tt\purple {Solution }$

$( {{ \frac{1}{4} }^{3} \times { \frac{1}{6} }^{3} \div { \frac{1}{2} }^{ 3}})^{ - 1}$

$( { \frac{1}{64} \times \frac{1}{216} \div \frac{1}{8}})^{ - 1}$

$( { \frac{1}{64} \times \frac{1}{216} \times 8})^{ - 1}$

${ \frac{1}{8} \times \frac{1}{216} }^{ - 1}$

${ \frac{1}{1728}}^{ - 1}$

$1728$

Note :- as the power is in negative (-) form of each fraction we have to make it positive (+) .Thus to make it positive we have to reverse that fraction .

Example :-

• if the fraction is like this

${ \frac{2}{3} }^{ - 2}$

• it is in negative form .To make it positive we have to reverse it. if we reverse it we will get
• ${ \frac{3}{2} }^{2}$