Simplify ((6y^3)^4)/(2y^7)

Problem

((6*y3)4)/(2*y7)

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)/(2*y7)

2. Apply the power of a power rule to the variable in the numerator by multiplying the exponents.

(1296*y12)/(2*y7)

3. Divide the coefficients by calculating the quotient of 1296 and 2

(648*y12)/(y7)

4. Apply the quotient rule for exponents by subtracting the exponent in the denominator from the exponent in the numerator.

648*y(12−7)

5. Simplify the exponent to find the final result.

648*y5

Final Answer

((6*y3)4)/(2*y7)=648*y5

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