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

Problem

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

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*y^3)^4=6^4⋅(y^3)^4

2. Simplify the exponents in the numerator using the power of a power rule, which states (a^m)^n=a^(m⋅n)

6^4⋅y^(3⋅4)=1296*y^12

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

(1296*y^12)/(2*y^3)

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

1296/2=648

y^(12−3)=y^9

Final Answer

((6*y^3)^4)/(2*y^3)=648*y^9

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