Why what number should 5 to the power -1 so that

To find the number that, when multiplied by \(5^{-1}\), equals \(-7^{-1}\), we can start by rewriting the expressions in a simpler form.

Understanding the Exponents

The expression \(5^{-1}\) means \(\frac{1}{5}\) and \(-7^{-1}\) means \(-\frac{1}{7}\). So, we need to find a number \(x\) such that:

Setting Up the Equation

The equation can be set up as follows:

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

Solving for x

To isolate \(x\), we can multiply both sides of the equation by \(5\):

• Left side: \(x\)
• Right side: \(-\frac{5}{7}\)

This gives us:

x = -\frac{5}{7}

Final Answer

Thus, the number that should be multiplied by \(5^{-1}\) to equal \(-7^{-1}\) is \(-\frac{5}{7}\).