Questions: Exponents Evaluating an expression with a negative exponent: Positive fraction b Rewrite the following without an exponent. (5/7)^-2

Solution Steps

To rewrite the expression \(\left(\frac{5}{7}\right)^{-2}\) without an exponent, we can use the property of negative exponents which states that \(a^{-n} = \frac{1}{a^n}\). Applying this property, we can rewrite the given expression as a positive exponent in the denominator.

1. Recognize that a negative exponent indicates the reciprocal of the base raised to the positive exponent.
2. Rewrite the expression using the reciprocal property.

We start with the expression \(\left(\frac{5}{7}\right)^{-2}\). Using the property of negative exponents, we can rewrite it as: \[ \left(\frac{5}{7}\right)^{-2} = \frac{1}{\left(\frac{5}{7}\right)^{2}} \]

Next, we calculate \(\left(\frac{5}{7}\right)^{2}\): \[ \left(\frac{5}{7}\right)^{2} = \frac{5^2}{7^2} = \frac{25}{49} \]

Now, we take the reciprocal of \(\frac{25}{49}\): \[ \frac{1}{\frac{25}{49}} = \frac{49}{25} \]

Calculating the decimal value of \(\frac{49}{25}\) gives us: \[ \frac{49}{25} = 1.96 \]

Final Answer