What is 3y to the 4th power divided by 6y to the negative 4 power
(3y)^4/(6y)^-4 = 3^4*6^4*y^8
= 104,976 y^8
If you meant
3*y^4/(6*y^-4), that is
(1/2)^4 y^8
= (1/16) y^8
Writing out algebraic terms is not a good idea. You need to show parentheses where needed.
To simplify the expression (3y)^4 / (6y)^(-4), we can follow these steps:
Step 1: Simplify the numerator
Raise 3y to the 4th power:
(3y)^4 = 3^4 * y^4 = 81y^4
Step 2: Simplify the denominator
Raise 6y to the -4th power:
(6y)^(-4) = 6^(-4) * y^(-4) = 1/(6^4 * y^4) = 1/(1296y^4)
Step 3: Divide the numerator by the denominator
(81y^4) / (1/(1296y^4))
Division by a fraction is equivalent to multiplying by its reciprocal, so we can rewrite the expression as:
(81y^4) * (1296y^4 / 1)
Step 4: Simplify the expression
Multiplying the numbers:
81 * 1296 = 104,976
Multiplying the variables:
y^4 * y^4 = y^(4 + 4) = y^8
Putting it all together, the simplified expression is:
104,976y^8