Question

evaluate : 3^-2 × [(5/4)^-1 - (10/3)^-1] pls answer it in a notebook pls​

Answer 1

Answer:

$the \: \: answer \: \: is \: \: - \frac{1}{18}$

Answer 2

Answer:

1/18 Ans..

Step-by-step explanation:

$\huge\sf\blue{Question:} \:$

$\displaystyle{ \implies \: {3}^{ - 2} \times \: (( \frac{5}{4}) {}^{ - 1} - ( \frac{10}{3} ) {}^{ - 1} )}$

$\huge\sf\blue{Solution:} \:$

As we know that,

$\displaystyle{ \sf{ {a}^{ - n} = \frac{1}{ {a}^{n} } }}$

So,

$\displaystyle{ \implies {3}^{ - 2} \times ( \frac{4}{5} - \frac{10}{3} )}$

$\sf\displaystyle{ \implies \: \frac{1}{3 \times 3} \times ( \frac{8 - 3}{10} }) \: \: \: (LCM \: = 10)$

$\displaystyle{ \implies \: \frac{1}{9} \times \cancel \frac{5}{10} }$

$\displaystyle{ \implies \: \frac{1}{9} \times \frac{1}{2} }$

$\sf\displaystyle{ \implies \: \frac{1}{18} \: \: ans...}$

$\huge\sf\blue{More \: Information :}$

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

Note:

Picture is also attached.