Solve it.Find the value of (1/2)^-2 + (1/3)^-2 + (1/2)^-2

1.	Solve it.Find the value of (1/2)^-2 + (1/3)^-2 + (1/2)^-2
Answer» We have given $\large{\bf{\green{(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}}}}$ . So to solve these type of questions, we REQUIRED some formulas of Exponent. In this question, we will use a formula which says that $(\frac{1}{n})^{-m}$ can be written as ${n}^{m}$ . _______________________ Let's understand that what does this formula SAYING: This formula says that, if power of any number is in negative form and if we will reverse the number, then the power became positive. Similarly, in this question also, we have given 3 NUMBERS (in fraction form) and powers are negative. So for solving further, we need to make power positive. USING this formula (mentioned above), if we reverse the number then power became positive. _______________________ Considering above formula: $\large{\bf{(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}}}$ $\implies\large{\bf{2^2+3^2+4^2}}$ $\implies\large{\bf{4+9+16}}$ $\implies\large{\bf{13+16}}$ $\implies\large{\bf{29}}$ _______________________ KNOW more formulas related to this type of questions: $\large{\sf{(\frac{a}{b})^m\times(\frac{a}{b})^n~=~(\frac{a}{b})^{m+n}}}$ $\large{\sf{\bigg[(\frac{a}{b})^m\bigg]^n~=~(\frac{a}{b})^{mn}}}$ $\large{\sf{(\frac{a}{b})^m\times(\frac{c}{d})^m~=~\bigg({\frac{a}{b}\times {\frac{c}{d}\bigg)^m}}}}$ $\large{\sf{(\frac{a}{b})^m\div (\frac{a}{b})^n~=~(\frac{a}{b})^{m-n}}}$

Answer»

We have given $\large{\bf{\green{(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}}}}$ . So to solve these type of questions, we REQUIRED some formulas of Exponent. In this question, we will use a formula which says that $(\frac{1}{n})^{-m}$ can be written as ${n}^{m}$ .

_______________________

Let's understand that what does this formula SAYING:

This formula says that, if power of any number is in negative form and if we will reverse the number, then the power became positive. Similarly, in this question also, we have given 3 NUMBERS (in fraction form) and powers are negative. So for solving further, we need to make power positive. USING this formula (mentioned above), if we reverse the number then power became positive.

_______________________

Considering above formula:

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

$\implies\large{\bf{2^2+3^2+4^2}}$

$\implies\large{\bf{4+9+16}}$

$\implies\large{\bf{13+16}}$

$\implies\large{\bf{29}}$

_______________________

KNOW more formulas related to this type of questions:

$\large{\sf{(\frac{a}{b})^m\times(\frac{a}{b})^n~=~(\frac{a}{b})^{m+n}}}$
$\large{\sf{\bigg[(\frac{a}{b})^m\bigg]^n~=~(\frac{a}{b})^{mn}}}$
$\large{\sf{(\frac{a}{b})^m\times(\frac{c}{d})^m~=~\bigg({\frac{a}{b}\times {\frac{c}{d}\bigg)^m}}}}$
$\large{\sf{(\frac{a}{b})^m\div (\frac{a}{b})^n~=~(\frac{a}{b})^{m-n}}}$