Question

(1/2) ^ - 3 + (1/3) ^ - 2 + (1/4) ^ - 2​

Answer 1

Answer:

((1/3)(-2)-(1/2)(-3))/(1/4)(-2)  

Final result :

 1            

—— = 0.06250  

16            

Step by step solution :

Step  1  :

                1

Simplify   —

                4

Equation at the end of step  1  :

 1      1    1

{—}-2-({—}-3)—-2)

 3      2(   4

Step  2  :

2.1     4 = 22 (4)-2 = (22)(-2) = (2)(-4)

Equation at the end of step  2  :

 1      1                    1

{—}-2-({—}-3)———————

 3      2               (2)(-4)

Step  3  :

          1

Simplify   —

          2

Equation at the end of step  3  :

 1       1                       1    

{—}-2 - (—)-3)) ÷ ———————

 3       2                   (2)(-4)

Equation at the end of step  4  :

 1                 1                          1    

{—}-2 - ———————) ÷ ———————

 3         (2)(-3)                      (2)(-4)  

Step  5  :

                1

Simplify   —

                3

Equation at the end of step  5  :

  1           1          1    

((—)-2) -  ———————) ÷ ———————

  3        (2)(-3)     (2)(-4)  

Step  6  :

Equation at the end of step  6  :

    1          1          1    

(——————— -  ———————) ÷ ———————

 (3)(-2)     (2)(-3)     (2)(-4)  

Step  7  :

Adding fractions which have a common denominator :

7.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

9 - (8)     1

———————  =  —

  1        1

Equation at the end of step  7  :

1      1    

— ÷ ———————

1   (2)(-4)  

Step  8  :

                 1    

Divide  1  by  ———————

              (2)(-4)  

Final result :

 1            

—— = 0.06250  

16            

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Answer 2

Answer:

$\purple{\star} \: {\large{\underline{\boxed{\tt{33}}}}}$

Step-by-step explanation:

$\diamond \: {\large{\underline{\underline{\sf{Concept:-}}}}}$

Negative Exponent Rule:- To change a negative exponent to positive we need to flip the value into a reciprocal.

━━━━━━━━━━━━━━━━━━━━━━

$\large{\sf{\bigg(\dfrac{1}{2}\bigg)^{ - 3} + {\bigg(\dfrac{1}{3}\bigg)^{ - 2} + {\bigg(\dfrac{1}{4}\bigg)^{ - 2}}}}}$

$\large{\sf{\leadsto{\bigg(\dfrac{2}{1}\bigg)^{3} + {\bigg(\dfrac{3}{1}\bigg)^{2} + {\bigg(\dfrac{4}{1}\bigg)^{2}}}}}}$

$\large{\sf{\leadsto{\bigg(2{\bigg)^{3} + {\bigg(3{\bigg)^{2} + {\bigg(4{\bigg)^{2}}}}}}}}}$

$\large{\sf{\leadsto{\bigg(2 \times 2 \times 2{\bigg) + {\bigg(3 \times 3{\bigg) + {\bigg(4 \times 4{\bigg)}}}}}}}}$

$\large{\sf{\leadsto{8 + 9 + 16}}}$

$\large{\gray{\sf{\leadsto{33}}}}$