Question

Hello Everyone, Hope you are fine.
My question is this - 5^{-1} * x = (-7)^{-1}
In which I got the answer as - \frac{5}{-7}
But in my Textbook the answer is \frac{-5}{7} , So are those both same and can you please solve and show the steps?
And can a rational number be \frac{x}{-y}

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given Equation:

$\rm \longrightarrow {5}^{ - 1} \cdot x = { - 7}^{ - 1}$

As we know that:

$\rm\longrightarrow {x}^{ - 1} = \dfrac{1}{x}$

$\rm \longrightarrow \dfrac{1}{5} \cdot x = \dfrac{ - 1}{7}$

Multiplying both sides by 5, we get:

$\rm \longrightarrow x = \dfrac{ - 1}{7} \times 5$

$\rm \longrightarrow x = \dfrac{ - 5}{7}$

★ So, the value of x is -5/7. (Answer)

$\textsf{\large{\underline{Learn More}:}}$

Laws Of Exponents: If a, b are positive real numbers and m, n are rational numbers, then the following results hold.

$\rm 1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\rm 2. \: \: ({a}^{m})^{n} = {a}^{mn}$

$\rm 3. \: \: \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\rm4. \: \: {a}^{m} \times {b}^{m} = {(ab)}^{m}$

$\rm5. \: \: \bigg(\dfrac{a}{b} \bigg)^{m} = \dfrac{ {a}^{m} }{ {b}^{m} }$

$\rm6. \: \: {a}^{ - n} = \dfrac{1}{ {a}^{n} }$

$\rm7. \: \: {a}^{n} = {b}^{n} \rightarrow a = b, n \neq0$

$\rm8. \: \: {a}^{m} = {a}^{n} \rightarrow m = n, a \neq 1$

Answer 2

$\gray{ \bold{ \underline{ \sf \: question}}}$

➽ Equation is

➽ 5^-1 •x = 7^-1

Solution

We know

➽ x^-1 = 1/x

➽ 1/5 • x = -1/7

Multiply 5 by both side

➽ x = -1/7×5

➽ x = -5/7

Answer is -5/7