Simplify (x^2(2x)^4)/(x^3)

Problem

(x2*(2*x)4)/(x3)

Solution

1. Apply the power of a product rule to the term (2*x)4 by raising both the coefficient and the variable to the fourth power.

(2*x)4=2⋅x4

2=16

2. Substitute the simplified term back into the expression.

(x2⋅16*x4)/(x3)

3. Apply the product rule for exponents to the numerator by adding the exponents of the x terms.

x2⋅x4=x(2+4)

x6

(16*x6)/(x3)

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

(x6)/(x3)=x(6−3)

x3

Final Answer

(x2*(2*x)4)/(x3)=16*x3

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