Teanne Shayla S. Francisco Annie says that \( \frac{7}{2}^{2} \) equals \( 1^{3} \) because she can she can divide 7 s and subtract the exponents. Writes an explauation so that Annie will whderstand why she is wrong and how to get the correct answer.

Hi Annie! Let's take a closer look at the expression \( \frac{7}{2}^{2} \) and see why it doesn't equal \( 1^{3} \). First, let's break down what \( \frac{7}{2}^{2} \) means. When you see a fraction raised to a power, you can apply the exponent to both the numerator and the denominator. So: \[ \frac{7}{2}^{2} = \frac{7^{2}}{2^{2}} \] Now, let's calculate \( 7^{2} \) and \( 2^{2} \): - \( 7^{2} = 49 \) - \( 2^{2} = 4 \) So, we have: \[ \frac{7^{2}}{2^{2}} = \frac{49}{4} \] Now, let's look at \( 1^{3} \). Any number raised to any power is still that number, and since \( 1 \) raised to any power is still \( 1 \): \[ 1^{3} = 1 \] Now we can compare the two results: - \( \frac{7}{2}^{2} = \frac{49}{4} \) - \( 1^{3} = 1 \) Clearly, \( \frac{49}{4} \) is not equal to \( 1 \). The mistake you made was in thinking that you could divide the numbers and subtract the exponents in a way that would lead to \( 1^{3} \). Instead, you need to apply the exponent to both the numerator and the denominator separately. So, the correct answer is: \[ \frac{7}{2}^{2} = \frac{49}{4} \quad \text{and} \quad 1^{3} = 1 \] These two values are not equal. I hope this helps you understand why \( \frac{7}{2}^{2} \) does not equal \( 1^{3} \)!