Question

Can anyone help me out with this?​

Answer 1

`{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}`

`\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}`

`\bullet \sf \: {(a + b)}^(ab)`

Putting value of a as 3 and b as -2, we get :

`\longrightarrow \sf \: {( 3 + (- 2))}^(3 * - 2)`

`\longrightarrow \sf \: {( 3 - 2)}^(3 * - 2)`

`\longrightarrow \sf \: {( 1)}^( - 6)`

• Using negative Exponents Law

`\longrightarrow \sf \frac{1}{ {1}^(6) }`

`\longrightarrow \sf (1)/( 1 * 1 * 1 * 1 * 1 * 1 )`

`\longrightarrow \sf (1)/( 1 )`

`\longrightarrow \sf \purple{1}`

`{\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}`

`\star\:{\underline{\underline{\sf{\red{Solution:}}}}}`

`\bullet \sf \: \frac{ {8}^( - 1) * {5}^(3) }{ {2}^( - 4)}`

`\longrightarrow \sf \: {8}^( - 1) * {5}^(3) * \frac{1}{{2}^( - 4)}`

• Using negative Exponents Law

`\longrightarrow \sf \: {8}^( - 1) * {5}^(3) * {2}^(4)`

`\longrightarrow \sf \: {8}^( - 1) * 5 * 5 * 5 * {2}^(4)`

`\longrightarrow \sf \: {8}^( - 1) * 125 * {2}^(4)`

`\longrightarrow \sf \: {8}^( - 1) * 125 * 2 * 2 * 2 * 2`

• Using negative Exponents Law

`\longrightarrow \sf \: \frac{1}{ \cancel{8}_(4)} * 125 * \cancel{2}_(1) * 2 * 2 * 2`

`\longrightarrow \sf \: (1)/( \cancel4_(2)) * 125 * \cancel{2}_(1) * 2 * 2`

`\longrightarrow \sf \: (1)/( \cancel2) * 125 * \cancel{2} * 2`

`\longrightarrow \sf \: 125 * 2`

`\longrightarrow \sf \red{ 250}`

`{\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}`

`\star\:{\underline{\underline{\sf{\green{Solution(1):}}}}}`

`\bullet \sf ( √(32) + √(48) )/( √(8) + √(12) )`

`\longrightarrow \sf ( √(4 * 4 * 2) + √(4 * 4 * 3) )/( √(2 * 2 * 2) + √(2 * 2 * 3) )`

`\longrightarrow \sf \frac{ \sqrt{ {4}^(2) * 2} + \sqrt{ {4}^(2) * 3} }{ \sqrt{ {2}^(2) * 2} + \sqrt{ {2}^(2) * 3} }`

`\longrightarrow \sf ( 4√( 2) + 4 √( 3) )/( 2√( 2) +2 √( 3) )`

`\longrightarrow \sf \frac{ \cancel{ 4}_(2)(√( 2) + √( 3)) }{ \cancel{2}(√( 2) + √( 3)) }`

`\longrightarrow \sf \frac{ 2 \: \cancel{(√( 2) + √( 3)) } }{ \cancel{(√( 2) + √( 3))} }`

`\longrightarrow \sf \green{2}`

`\star\:{\underline{\underline{\sf{\blue{Solution(2):}}}}}`

`\bullet \sf ( √(5) + √(3) )/( √(80) + √(48) - √(45) - √(27) )`

`\begin{gathered} \longrightarrow \sf ( √(5) + √(3) )/( √(4 * 4 * 5) + √(4 * 4 * 3) - √(3 * 3 * 5) - √(3 * 3 * 3) ) \end{gathered}`

`\begin{gathered}\longrightarrow \sf \frac{ √(5) + √(3) }{ \sqrt{ {4}^(2) * 5} + \sqrt{ {4}^(2) * 3} - \sqrt{ {3}^(2) * 5} - \sqrt{ {3}^(2) * 3} } \end{gathered}`

`\longrightarrow \sf ( √(5) + √(3) )/(4 √( 5) + 4 √( 3) - 3√( 5) - 3√( 3) )`

`\longrightarrow \sf ( √(5) + √(3) )/(4 √( 5) - 3√( 5) + 4 √( 3) - 3√( 3) )`

`\longrightarrow \sf \frac{ \cancel{ √(5) + √(3)} }{ \cancel{√( 5) + √( 3) } }`

`\longrightarrow \blue{1}`

`{\large{\textsf{\textbf{\underline{\underline{Answers :}}}}}}`

• Question 1 -
`\purple{1}`

• Question 2 -
`\red{250}`

• Question 3(1) -
`\green{2}`

• Question 3(2) -
`\blue{1}`

`{\large{\textsf{\textbf{\underline{\underline{ Concept \: :}}}}}}`

★ Negative Exponents Law -

`\bullet \sf \: {a}^( - m) = \frac{1}{ {a}^(m) }`

★
`√(32)` can be written as
`4 √(2)`

‣
`√(48)` can be written as
`4 √(3)`

‣
`√(8)` can be written as
`2 √(2)`

‣
`√(12)` can be written as
`2 √(3)`

‣
`√(80)` can be written as
`4 √(5)`

‣
`√(48)` can be written as
`4 √(3)`

‣
`√(45)` can be written as
`3 √(5)`

‣
`√(27)` can be written as
`3 √(3)`

★ During Addition and Subtraction

• minus (-) minus (-) gives plus (+)

• minus (-) plus (+) gives minus (-)

• plus (+) minus (-) gives minus (-)

• plus (+) plus (+) gives plus (+)

• Also the sign of the resultant term depends upon the sign of the largest number.

`{\large{\textsf{\textbf{\underline{\underline{ Note \: :}}}}}}`

• Swipe to see the full answer.

`\begin{gathered} {\underline{\rule{330pt}{3pt}}} \end{gathered}`