Math, asked by supriya1918, 1 month ago

express each of the following in positive exponents only​

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Answers

Answered by deshmukhjiya76
0

Answer:

a.

 {5}^{6}  {3}^{ - 4}

Step-by-step explanation:

a.

Answered by itsPapaKaHelicopter
2

\sf \colorbox{lightgreen} {Ans.a}

\sf \colorbox{god} {Given:-} \frac{ {5}^{ - 2}  \times  {3}^{2} }{ {5}^{ - 4}  \times  {3}^{ - 6} }

Express the expression in positive exponents only:-

⇒\frac{ {5}^{ - 2}  \times  {3}^{2} }{ {5}^{ - 4}  \times  {3}^{ - 6} }   =  \frac{ {3}^{2} \times  {5}^{4}  \times  {3}^{6}  }{ {5}^{2} }  \:  \:  \:  \:  \:  \: [ {a}^{ - m}  =  \frac{1}{ {a}^{m} } ]

Hence,

⇒ \frac{ {5}^{ - 2} \times  {3}^{2}  }{ {5}^{ - 4}  \times  {3}^{ - 6} }  =  \frac{ {3}^{2}  \times  {5}^{4}  \times  {3}^{6} }{ {5}^{2} }

\sf \colorbox{lightgreen} {Ans.b}

\text{Given:-}  \:  \frac{ {x}^{ - 2}   \times {y}^{ - 4}  \times  {z}^{ - 3} }{xyz}

 \textbf{To Find:- exponents the following}

solve:-

\text{As we know \: }  \frac{ {x}^{a} }{ {x}^{b} }  = x(a - b)

Now,

⇒x - 2 - 1 \times y - 4 - 1 \times z - 3 - 1 =  {x}^{ - 3}  \times  {y}^{5}  \times  {z}^{ - 4}

⇒ \frac{1}{ {x}^{3} \times  {y}^{5}  \times  {z}^{4}  }  \:  \: [ {x}^{ - a}  =  \frac{1}{ {x}^{a} } ]

 =  \frac{1}{ {x}^{3} \times  {y}^{5}  \times  {z}^{4}  }

\sf \colorbox{lightgreen} {Ans.c}

\sf \colorbox{god} {Given:-}( - 3 {)}^{2}  \times ( {5}^{2}  {)}^{ - 2}

To Find:- Express the following in positive exponents only.

Solve:-

⇒( - 3 {)}^{2}  \times ( {5}^{2}  {)}^{ - 2}

⇒( - 3 {)}^{2}  \times  { \left(  \frac{1}{ {5}^{2} } \right) \]}^{2}

⇒( - 3 {)}^{2}  \times  { \left( \frac{1}{25}  \right) \]}^{2}

 =  { \left(  \frac{ - 3}{25} \right) \]}^{2}

\sf \colorbox{lightgreen} {Ans.d}

\sf \colorbox{god} {Given:-}\[ \left[  ( -  {4}^{2}  {)}^{3}  \div ( {2}^{2}  {)}^{4} \right] \] \times ( {3}^{2}  {)}^{ - 2}

solve:-

⇒\[ \left[  ( -  {4}^{2}  {)}^{3}  \div ( {2}^{2}  {)}^{4} \right] \] \times ( {3}^{2}  {)}^{ - 2}

⇒[ {16}^{3}  \div  {4}^{4} ]  \times (9 {)}^{ - 2}  \:   \:  \: \: [ {a}^{ - m}  =  \frac{1}{ {a}^{m} } ]

⇒[ {16}^{3}  \div  {16}^{2} ]  \times  \frac{1}{(9 {)}^{2} }

⇒ \frac{16}{81}  =   \frac{ {2}^{4} }{ {3}^{4} }

 \\  \\  \\  \\ \sf \colorbox{lightgreen} {\red★ANSWER ᵇʸɴᴀᴡᴀʙ}

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