To simplify the expression \((4x^{3}y^{-4})^{-2}\), we will apply the property of exponents \((a^m)^{-n} = a^{-mn}\).
Starting with the expression:
\[ (4x^{3}y^{-4})^{-2} \]
we can distribute the exponent \(-2\) to each term inside the parentheses:
\[ = 4^{-2} (x^{3})^{-2} (y^{-4})^{-2} \]
Now, let's simplify each part:
- \(4^{-2} = \frac{1}{4^2} = \frac{1}{16}\)
- \((x^{3})^{-2} = x^{-6}\)
- \((y^{-4})^{-2} = y^{8}\)
Putting this all together, we get:
\[ = \frac{1}{16} \cdot x^{-6} \cdot y^{8} \]
Now, we can express \(x^{-6}\) as \(\frac{1}{x^{6}}\):
\[ = \frac{y^{8}}{16x^{6}} \]
Thus, the simplified form of the expression \((4x^{3}y^{-4})^{-2}\) is:
\[ \frac{y^{8}}{16x^{6}} \]
1 answer