To simplify the expression \( (x \cdot y^3 \cdot z^4)^4 \), we apply the power of a product rule, which states that \( (a \cdot b \cdot c)^n = a^n \cdot b^n \cdot c^n \).
Applying this to our expression:
\[ (x \cdot y^3 \cdot z^4)^4 = x^4 \cdot (y^3)^4 \cdot (z^4)^4 \]
Now, we simplify each term:
- For \( x^4 \), it stays as \( x^4 \).
- For \( (y^3)^4 \), we use the power rule \( (a^m)^n = a^{m \cdot n} \): \[ (y^3)^4 = y^{3 \cdot 4} = y^{12} \]
- For \( (z^4)^4 \): \[ (z^4)^4 = z^{4 \cdot 4} = z^{16} \]
Now we can combine all the parts: \[ (x \cdot y^3 \cdot z^4)^4 = x^4 \cdot y^{12} \cdot z^{16} \]
Therefore, the simplified expression is: \[ C. \quad x^4 \cdot y^{12} \cdot z^{16} \]
So the answer is C. \( x^4 \cdot y^{12} \cdot z^{16} \).
3 answers