Question

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Answer 1

Answer:

30

Step-by-step explanation:

please follow the above attachment for the solution

Answer 2

Given :

$\displaystyle {\sf \Big(6^{-1}-8^{-1}\Big)^{-1}+\Big(2^{-1}-3^{-1}\Big)^{-1}}$

Explanation:

A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as $\sf \frac{1}{x^n}$ For example,

2⁻⁴ = $\sf \frac{1}{2^4}$ =$\sf\frac{1}{16}$ .

Solution :

$\rightarrow \displaystyle {\sf \Big(6^{-1}-8^{-1}\Big)^{-1}+\Big(2^{-1}-3^{-1}\Big)^{-1}}$

$\rightarrow \displaystyle {\sf \Big(\frac{1}{6}-\frac{1}{8}\Big)^{-1}+\Big(\frac{1}{2}-\frac{1}{3}\Big)^{-1}}$

$\rightarrow \displaystyle {\sf \Big(\frac{(1 \times 8)-(1 \times 6)}{(6 \times 8)}\Big)^{-1}+\Big(\frac{(1 \times 3)-(1 \times 2)}{(2 \times 3)}\Big)^{-1}}$

$\rightarrow \displaystyle {\sf \Big(\frac{8-6}{48}\Big)^{-1}+\Big(\frac{3-2}{6} \Big)^{-1}}$

$\rightarrow \displaystyle {\sf \Big(\frac{\cancel{2}^{1}}{\cancel{48}_{24}}\Big)^{-1}+\Big(\frac{1}{6} \Big)^{-1}}$

$\rightarrow \displaystyle {\sf \Big(\frac{1}{24}\Big)^{-1}+\Big(\frac{1}{6} \Big)^{-1}}$

$\rightarrow \sf 24+6 \implies 30$

Required Answer :

Simplified form of$\displaystyle {\sf \Big(6^{-1}-8^{-1}\Big)^{-1}+\Big(2^{-1}-3^{-1}\Big)^{-1}}$ is $\underline {\sf 30}$