Final answer:
The expression equivalent to (xy⁷z³)⁶ is x⁶y¹⁴²z¹⁸.
Step-by-step explanation:
The expression equivalent to (xy⁷z³)⁶ is found by applying the power of a power rule in exponents. Here, we have a product inside the parentheses raised to the sixth power. Thus, each factor's exponent is multiplied by six:
x⁶(y⁷)⁶(z³)⁶
Now, we calculate the new exponents by multiplying:
- x to the power of 1 times 6 becomes x⁶
- y to the power of 7 times 6 becomes y¹⁴²
- z to the power of 3 times 6 becomes z¹⁸
So, the simplified and equivalent expression is x⁶y¹⁴²z¹⁸.