which expression is equivalent to 10q^5w^7/2w^3 ⋅ (4q^6)^2 for all values of q and w where the expression is defined?
To simplify the expression, we can start by simplifying the term 4q^6 which is raised to the power of 2.
(4q^6)^2 = 4^2 * (q^6)^2 = 16 * q^12 = 16q^12
Now, let's simplify the entire expression:
10q^5w^7/2w^3 * (4q^6)^2 = (10q^5w^7/2w^3) * 16q^12
Combining like terms, this simplifies to:
(10 * 16 * q^5 * q^12 * w^7) / (2 * w^3)
= 160q^17w^7 / 2w^3
Since we have a common factor of 2, we can simplify further:
= 80q^17w^7/w^3
= 80q^17w^(7-3)
= 80q^17w^4
Therefore, the expression is equivalent to 80q^17w^4 for all values of q and w where the expression is defined.