Question

you can please tell me the answers ​

Answer 1

Answer:

hope it helps you matee

Step-by-step explanation:

a power m×a power n=a power m+n

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{To\:Find:-}}}$

• $\rm(i) \: \: {2}^{ - 3} \times {2}^{ - 2}$

• $\rm(ii) \: \: {7}^{ - 2} \times {7}^{ 5}$

• $\rm(iii) \: \: {3}^{ 4} \times {3}^{ - 5}$

• $\rm(iv) \: \: {7}^{ 5} \times {7}^{ - 4}\times {7}^{-6}$

• $\rm(v) \: \: {m}^{ 5} \times {m}^{ - 10}$

• $\rm(vi) \: \: {(-5)}^{ - 3} \times {(-5)}^{ - 4}$

$\bf{\underline{\underline\green{Solution:-}}}$

$\rm(i) \: \: {2}^{ - 3} \times {2}^{ - 2}$

By using the identity

$\boxed{ \rm \implies{ a}^{m} \times {a}^{n} = {a}^{m + n} }$

${ \rm \implies{ 2}^{ - 3} \times {2}^{ - 2}}$

${ \rm \implies{ 2}^{ - 3 + ( - 2)} }$

${ \rm \implies{ 2}^{ - 3 - 2} }$

${ \rm \implies{ 2}^{ - 5} }$

__________________

$\rm(ii) \: \: {7}^{ - 2} \times {7}^{ 5}$

By using the identity

$\boxed{ \rm \implies{ a}^{m} \times {a}^{n} = {a}^{m + n} }$

${ \rm \implies{ 7}^{ - 2} \times {7}^{ 5}}$

${ \rm \implies{ 7}^{ - 2 + ( 5)} }$

${ \rm \implies{ 7}^{ - 2 + 5} }$

${ \rm \implies{ 7}^{ 3} }$

___________________

$\rm(iii) \: \: {3}^{ 4} \times {3}^{ - 5}$

By using the identity

$\boxed{ \rm \implies{ a}^{m} \times {a}^{n} = {a}^{m + n} }$

${ \rm \implies{ 3}^{ 4} \times {3}^{ - 5}}$

${ \rm \implies{ 3}^{ 4 + ( - 5)} }$

${ \rm \implies{ 3}^{ 4 - 5} }$

${ \rm \implies{ 3}^{ - 1 } }$

___________________

$\rm(iv) \: \: {7}^{ 5} \times {7}^{ - 4} \times {7}^{-6}$

By using the identity

$\boxed{ \rm \implies{ a}^{m} \times {a}^{n} = {a}^{m + n} }$

${ \rm \implies{ 7}^{ 5} \times {7}^{ - 4}\implies {7}^{-6}}$

${ \rm \implies{ 7}^{ 5 + ( - 4)+ (-6)} }$

${ \rm \implies{ 7}^{ 5 - 4-6} }$

${ \rm \implies{ 7}^{ -5} }$

___________________

$\rm(v) \: \: {m}^{ 5} \times {m}^{ - 10}$

By using the identity

$\boxed{ \rm \implies{ a}^{m} \times {a}^{n} = {a}^{m + n} }$

${ \rm \implies{ m}^{ 5} \times {m}^{ - 10}}$

${ \rm \implies{ m}^{ 5 + ( - 10)} }$

${ \rm \implies{ m}^{ 5 - 10} }$

${ \rm \implies{ m}^{ - 5} }$

____________________

${ \rm \implies {( - 5)}^{ - 3} \times {( - 5)}^{ - 4} }$

By using the identity

$\boxed{ \rm \implies{ a}^{m} \times {a}^{n} = {a}^{m + n} }$

${ \rm \implies {( - 5)}^{ - 3} \times {( - 5)}^{ - 4} }$

${ \rm \implies {( - 5)}^{ - 3 + ( - 4)} }$

${ \rm \implies {( - 5)}^{ - 3 - 4} }$

${ \rm \implies {( - 5)}^{ - 7} }$