Question

Simplify:
{(12)^1 + (13)^-1}/[(1/5)^-2 × {(1/5)^-1 + (1/8)^-1}^-1]​

Answer 1

Answer : 1/20

Step-by-step explanation:

Answer 2

Step-by-step explanation:

`\underline{\underline{\sf{➤\:\:Solution}}}`

`\sf \dashrightarrow \: ( \left(\left(12 \right)^( - 1) + \left(13 \right)^( - 1) \right) )/(\left( (1)/(5)\right) ^( - 2) *\left( \left( (1)/(5) \right) ^( - 1) +\left( (1)/(8) \right) ^( - 1) \right) ^( - 1))`

`\sf \dashrightarrow \: ( \left((1)/(12) + (1)/(13) \right) )/(\left( (5)/(1)\right) ^( 2) *\left( (5)/(1) + (8)/(1) \right) ^( - 1))`

• LCM of 12 and 13 is 156

`\sf \dashrightarrow \: ( \left((1 * 13 = 13)/(12 * 13 = 156) + (1 * 12 = 12)/(13 * 12 = 156) \right) )/(\ (25)/(1) *\left( (5 + 8)/(1) \right) ^( - 1))`

`\sf \dashrightarrow \: ( \left((13)/(156) + (12)/(156) \right) )/(\ (25)/(1) *\left( (13)/(1) \right) ^( - 1))`

`\sf \dashrightarrow \: ( \left((13 + 12)/(156) \right) )/(\ (25)/(1) *(1)/(13) )`

`\sf \dashrightarrow \: (25)/(156) / (25)/(13)`

`\sf \dashrightarrow \: \frac{ \cancel{25}}{156} * \frac{13}{ \cancel{25} }`

`\sf \dashrightarrow \: (13)/(156)`

`\sf \dashrightarrow \: (1)/(12)`

`\sf \dashrightarrow \: Answer = \underline{\boxed{ \sf{ (1)/(12) }}}`

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`\underline{\underline{\sf{★\:\:Laws\:of\: Exponents :}}}`

`\sf \: 1^(st) \: Law = \bigg( (m)/(n) \bigg)^(a) * \bigg( (m)/(n) \bigg)^(b) = \bigg( (m)/(n) \bigg)^(a + b)`

`\sf 2^(nd) \: Law =`

`\sf Case : (i) \: if \: a > b \: then, \bigg( (m)/(n)\bigg) ^(a) / \bigg( (m)/(n)\bigg)^(b) = \bigg( (m)/(n)\bigg)^(a - b)`

`\sf Case : (ii) \: if \: a < b \: then, \bigg( (m)/(n)\bigg) ^(a) / \bigg( (m)/(n)\bigg)^(b) = (1)/(\bigg( (m)/(n)\bigg)^(b - a))`

`\sf \: 3^(rd) \: Law = \bigg\{ \bigg( (m)/(n) \bigg)^(a) \bigg\}^(b) = \bigg( (m)/(n) \bigg)^(a * b) =\bigg( (m)/(n) \bigg)^(ab)`

`\sf \: 4^(th) \: Law = \bigg( (m)/(n) \bigg)^( - 1) = \bigg( (n)/(m) \bigg) =(n)/(m)`

`\sf \: 5^(th) \: Law = \bigg( (m)/(n) \bigg)^(0) = 1`