Final answer:
The equivalent expression for cd^4/c^2d^8 is 1/(cd^4) after applying the laws of exponents and simplification.
Step-by-step explanation:
The expression in question is cd^4/c^2d^8. To simplify this expression, we need to apply the laws of exponents and division of powers with the same base. We know that when we divide powers with the same base, we subtract the exponents. In our case:
c/c^2 simplifies to 1/c since c is equivalent to c^1, and when we subtract the exponents, we get c^(1-2) = c^(-1).
d^4/d^8 simplifies to d^(-4) for the same reason, giving us d^(4-8) = d^(-4).
Thus, when we combine these simplified terms, we cancel out the equivalent terms in the numerator and denominator, leaving us with the final expression 1/c^1d^4 or, more commonly written as, 1/(cd^4).
The given expression is cd4/c2d8. To simplify this expression, we can divide the variables c and d separately. Dividing c by c2 gives us 1/c, and dividing d4 by d8 gives us 1/d4. So, the equivalent expression is 1/cd4d4.