Question
Is nine to the 12th power times nine to the -3 power over nine to the third power equal to 9/6
Answers
GPT-4o mini
To simplify the expression \(\frac{9^{12} \times 9^{-3}}{9^3}\), we can use the properties of exponents.
1. First, we combine the exponents in the numerator:
\[
9^{12} \times 9^{-3} = 9^{12 + (-3)} = 9^{12 - 3} = 9^9.
\]
2. Next, we simplify the fraction:
\[
\frac{9^9}{9^3} = 9^{9 - 3} = 9^6.
\]
Now we have reduced the original expression to \(9^6\).
Next, we need to determine if \(9^6\) is equal to \(\frac{9}{6}\).
3. Calculate \(9^6\):
\[
9^6 = (3^2)^6 = 3^{12}.
\]
4. Calculate \(\frac{9}{6}\):
\[
\frac{9}{6} = \frac{3^2}{2 \times 3} = \frac{3}{2}.
\]
It's evident that \(9^6\), which equals \(3^{12}\), is not equal to \(\frac{3}{2}\).
Therefore, the final answer is:
\[
\frac{9^{12} \times 9^{-3}}{9^3} \neq \frac{9}{6}.
\]
1. First, we combine the exponents in the numerator:
\[
9^{12} \times 9^{-3} = 9^{12 + (-3)} = 9^{12 - 3} = 9^9.
\]
2. Next, we simplify the fraction:
\[
\frac{9^9}{9^3} = 9^{9 - 3} = 9^6.
\]
Now we have reduced the original expression to \(9^6\).
Next, we need to determine if \(9^6\) is equal to \(\frac{9}{6}\).
3. Calculate \(9^6\):
\[
9^6 = (3^2)^6 = 3^{12}.
\]
4. Calculate \(\frac{9}{6}\):
\[
\frac{9}{6} = \frac{3^2}{2 \times 3} = \frac{3}{2}.
\]
It's evident that \(9^6\), which equals \(3^{12}\), is not equal to \(\frac{3}{2}\).
Therefore, the final answer is:
\[
\frac{9^{12} \times 9^{-3}}{9^3} \neq \frac{9}{6}.
\]