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.

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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 $$ 1^{3} $$!
Annie, $$ \frac{7}{2}^{2} $$ is not equal to $$ 1^{3} $$ because you need to apply the exponent to both the numerator and the denominator separately. The correct calculation is $$ \frac{7}{2}^{2} = \frac{49}{4} $$ and $$ 1^{3} = 1 $$.

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.

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