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

Problem

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

Solution

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

(6*y3)4=6⋅(y3)4

2. Simplify the exponents in the numerator 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*y3)

4. Divide the coefficients and apply the quotient rule for exponents, which states (am)/(an)=a(m−n)

1296/2=648

y(12−3)=y9

Final Answer

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

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