Question

simplify (1/2)^-2+(1/3)^-2+(1/4)^-2​

Answer 1

Given:

An expression (1/2)^-2+(1/3)^-2+(1/4)^-2.

To find:

The simplified value of the given expression.

Solution:

To solve this question, first of all, we should know one of the properties of exponents and powers which is:

${ (\frac{a}{b}) }^{ - 2} = { (\frac{b}{a}) }^{ 2}$

Now,

Proceeding to the solution,

We have an expression,

${ (\frac{1}{2}) }^{ - 2} + { (\frac{1}{3}) }^{ - 2} + { (\frac{1}{4}) }^{ - 2}$

The above expression can be written as

${ (\frac{2}{1}) }^{ 2} + { (\frac{3}{1}) }^{2} + { (\frac{4}{1}) }^{ 2}$

( from the property of exponents and powers which is written above)

$= {2}^{2} + {3}^{2} + {4}^{2}$

$= 4 + 9 + 16$

$= 13 + 16$

$= 29$

So, the simplified value of the given expression is 29.