Let the number \(5^{-1}\) should be multiplied by \(x\)

According to the question:

\(x\times 5^{-1}=(-7)^{-1}\)

\(x\times \frac{1}{5}=\frac{1}{-7}\)[Using \(a^{-n}=\frac{1}{a^{n}}\)]

\(x=\frac{1}{-7}\times \frac{5}{1}=\frac{5}{-7}\)

Therefore \(5^{-1}\) should be multiplied by \(\frac{-5}{7}\)

Let the number be = x

So,

5^-1 × x = (-7)^-1

1/5 × x = 1/-7 (1/aⁿ = a^-n)

x = (-1/7) / (1/5)

= (-1/7) × (5/1) (1/a ÷ 1/b = 1/a × b/1)

= -5/7

Let the number should \(5^{-1}\) be multiplied by x

According to the question:

\(x\times 5^{-1}=(-7)^{-1}\)

\(x\times \frac{1}{5}=\frac{1}{-7}\)[Using \(a^{-n}=\frac{1}{a^{n}}\)]

\(x=\frac{1}{-7}\div \frac{5}{1}=\frac{5}{-7}\)

\(x=\frac{1}{-7}\times \frac{5}{1}=\frac{5}{-7}\)= \(-\frac{5}{7}\)[Using and \(\frac{1}{a}\div \frac{1}{b}=\frac{1}{a}\times \frac{b}{1}\)]

Therefore \(5^{-1}\) should be multiplied by \(\frac{-5}{7}\)

Let the number be x

So, 

5^-1 × x = (-7)^-1

1/5 × x = 1/-7

x = (-1/7) / (1/5)

= (-1/7) × (5/1)

= -5/7