Final answer:
We can simplify the given mathematical expression by using exponentiation rules or simplifying it by eliminating common factors. Both methods give us the same answer: 1/1024x⁻⁷ʸ.
Step-by-step explanation:
The given mathematical expression is (4x⁵ʸ/(16xy⁴)³. This can be simplified in two methods and both should give the same result.
For the first method, we can use exponentiation rules. The first exponentiation rule is that when dividing exponents of the same base, we subtract the exponent in the denominator from the one in the numerator. Here, x⁵ⁿ⁻⁴³ = x⁵ⁿ⁻¹² = x⁻⁷ʸ. The second rule is for the constants; 4/16³ = 4/4096 = 1/1024.
For the second method, we can see that there are common factors in the numerator and the denominator. This allows us to simplify the expression by eliminating these common factors. Here, we see that 4 and 16 have a common factor of 4; x⁵ʸ and xy⁴ have x as a common factor and y's as well. Now, we can rewrite it as (1x⁴ʸ/4²(x⁴)³ = x⁴ʸ/x¹² = x⁻⁸ʸ.
Both methods get the same answer and once simplified to lowest terms, the answer is
1/1024x⁻⁷ʸ
.
Learn more about Expression Simplification