Simplify ((6y^3)^4)/(2y^9)

Problem

((6*y3)4)/(2*y9)

Solution

1. Apply the power of a product rule to the numerator by raising both the coefficient and the variable to the fourth power.

(6*y3)4=6⋅(y3)4

2. Simplify the exponent using the power of a power rule, which states (am)n=a(m⋅n)

6⋅y(3⋅4)=1296*y12

3. Rewrite the expression with the simplified numerator over the original denominator.

(1296*y12)/(2*y9)

4. Divide the coefficients by calculating 1296 divided by 2

1296/2=648

5. Apply the quotient rule for exponents, which states (am)/(an)=a(m−n) to the variable y

(y12)/(y9)=y(12−9)=y3

6. Combine the results to find the final simplified form.

648*y3

Final Answer

((6*y3)4)/(2*y9)=648*y3

Want more problems? Check here!