Question

express each of the following in positive exponents only​

Answer 1

Answer:

a.

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

Step-by-step explanation:

a.

Answer 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}$

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

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

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

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