Question

friends please help me ​

Answer 1

Ans. (i)

$\textbf{Given:-} \: ( {2}^{ - 3} {)}^{2} \div ( - 4 {)}^{ - 3}$

Solve:-

$\[ \left[ ( {a}^{m} {)}^{n} = {a}^{mn} \textbf{ \: and \: } {a}^{ - m} = \frac{1}{am} \right] \]$

$⇒ {2}^{ - 3 \times 2} \div \frac{1}{( - 4 {)}^{3} }$

$⇒ {2}^{ - 6} \times \frac{( - 4 {)}^{3} }{1}$

$⇒ \frac{1}{ {2}^{6} } \times {( - 4)}^{3}$

$⇒ \frac{( - 4) \times ( - 4) \times ( - 4)}{2 \times 2 \times 2 \times 2 \times 2 \times 2}$

$⇒ \frac{ - 64}{64}$

$\text{Hence -1 is our correct answer}$

━━━━━━━━━━━━━━━━━━━━━━━

Ans. (ii)

$\textbf{Given:-} \: ( {3}^{8} \div {3}^{ - 6} ) \times ( {9}^{ - 2} {)}^{3}$

Solve:-

$\[ \left[ {a}^{m} + {a}^{n} = {a}^{m - n} \textbf{ \: and \: } ( {a}^{m} {)}^{n} = {a}^{mn} \right] \]$

$⇒ ({3}^{8 - ( - 6)} ) \times {9}^{ - 2 \times 3}$

$⇒ {3}^{8 + 3} \times ( {3}^{2} {)}^{ - 6} = {3}^{14} \times {3}^{ - 12}$

$⇒ {3}^{14 - 12} = {3}^{2} = 9$

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

Answer 2

Answer:

m

)

n

=a

mn

and a

−m

=

am

1

]

⇒ {2}^{ - 3 \times 2} \div \frac{1}{( - 4 {)}^{3} }⇒2

−3×2

÷

(−4)

3

1

⇒ {2}^{ - 6} \times \frac{( - 4 {)}^{3} }{1}⇒2

−6

×

1

(−4)

3

⇒ \frac{1}{ {2}^{6} } \times {( - 4)}^{3}⇒

2

6

1

×(−4)

3

⇒ \frac{( - 4) \times ( - 4) \times ( - 4)}{2 \times 2 \times 2 \times 2 \times 2 \times 2}⇒

2×2×2×2×2×2

(−4)×(−4)×(−4)

⇒ \frac{ - 64}{64}⇒

64

−64

\text{Hence -1 is our correct answer}Hence -1 is our correct answer

━━━━━━━━━━━━━━━━━━━━━━━

Ans. (ii)

\textbf{Given:-} \: ( {3}^{8} \div {3}^{ - 6} ) \times ( {9}^{ - 2} {)}^{3}Given:-(3

8

÷3

−6

)×(9

−2

)

3

Solve:-

\left[ {a}^{m} + {a}^{n} = {a}^{m - n} \textbf{ \: and \: } ( {a}^{m} {)}^{n} = {a}^{mn} \right][a

m

+a

n

=a

m−n