Question

please solve this question.​

Answer 1

AnsWer :

- 5 / 7.

QuestioN :

By what number should 5^-1 be multiplied so that product become ( - 7 )^-1 ?

To FinD :

The number.

SolutioN :

Let,

• The number be x , multiple with ( 5 )^-1 to get ( - 7 )^-1.

Our Equation become,

$\tt \dagger \: \: \: \: \: {(5)}^{ - 1} \times x = {( - 7)}^{ - 1}$

$\tt : \implies {(5)}^{ - 1} \times x = {( - 7)}^{ - 1}$

$\tt : \implies x = \dfrac{{( - 7)}^{ - 1} }{ {(5)}^{ - 1} }$

☛ ConcepT Used :

• a^x / b^x = ( a / b )^x.

Here,

• a = - 7.
• b = 5.
• x = - 1.

So, We can also write as.

$\tt : \implies x ={ \bigg(\dfrac{{ - 7} }{ {5} } \bigg)}^{ - 1}$

☛ ConcepT Used :

• ( a / b )^-1 = ( b / a )^1.

Where as,

• a = - 7.
• b = 5.

$\tt : \implies x ={ \bigg(\dfrac{{ 5} }{ { - 7} } \bigg)}^{ 1}$

$\tt : \implies x = - \dfrac{{ 5} }{ { 7} }$

✡ Therefore, the value of x is - 5 / 7.

VerificatioN :

Let,

• x = - 5 / 7.
• y = 5^-1.

$\tt : \implies x \times y = {( - 7)}^{ - 1}$

Taking LHS,

$\tt : \implies - \dfrac{5}{7} \times {(5)}^{ - 1}$

$\tt : \implies - \dfrac{ \cancel5}{7} \times \dfrac{1}{ \cancel5}$

$\tt : \implies - \dfrac{1}{7}$

RHS,

$\tt : \implies {( - 7)}^{ - 1}$

$\tt : \implies - \dfrac{1}{7}$

≛ Hence, LHS = RHS.

Answer 2

Answer:

-5/7

Step-by-step explanation:

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