Question

Plz Solve this with explanation .
PLZ
PLZ.​

Answer 1

Answer:

as all the powers are same so take the no

Step-by-step explanation:

1/3+1/4+1/5-1/6

take lcm of the denominator and solve it

game over....

Answer 2

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Given:}}}}}$

$\sf {\star { { \bigg(}\dfrac{1}{3} { \bigg)}}^{ - 2} + { \bigg(}{ \dfrac{1}{4}{ \bigg)} }^{ - 2} + { \bigg(} { \dfrac{1}{5}}{ \bigg)} ^{ - 2} - { \bigg(}{ \dfrac{1}{6}{ \bigg)} }^{ - 2}}$

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Solution:}}}}}$

$\\ \implies \sf { { \bigg(}\dfrac{1}{3} { \bigg)}}^{ - 2} + { \bigg(}{ \dfrac{1}{4}{ \bigg)} }^{ - 2} + { \bigg(} { \dfrac{1}{5}}{ \bigg)} ^{ - 2} - { \bigg(}{ \dfrac{1}{6}{ \bigg)} }^{ - 2}$

ㅤㅤㅤㅤㅤ

For any non-zero number,

$\bf \dfrac{1}{ {a}^{ - n} } = {a}^{n}$

$\\ \\ \implies \sf {3}^{2} + {4}^{2} + {5}^{2} - {6}^{2}$

ㅤㅤㅤㅤㅤ

Now, expand it

$\\ \implies \sf 3 \times 3 + 4 \times 4 + 5 \times 5 - 6 \times 6$

ㅤㅤㅤㅤㅤ

We will follow BODMAS, first we remove the brackets, then we will do division followed by multiplication addition and subtraction.

$\\ \\ \implies \sf 9 + 16 + 25 - 36$

$\\ \\ \implies \sf 25+ 25 - 36$

$\\ \\ \implies \sf 50 - 36$

$\\ \\{ \blue {\implies {\bf {14}}}}$

ㅤㅤㅤㅤㅤ

ㅤㅤㅤㅤㅤ

Law's of exponents :

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

ㅤㅤㅤㅤㅤ

_______________________________