Simplify ((2x^3)^2z^5)/(2z^9)

Problem

((2*x3)2*z5)/(2*z9)

Solution

1. Apply the power of a product rule to the term (2*x3)2 by squaring both the coefficient and the variable.

(2*x3)2=2⋅(x3)2

2⋅(x3)2=4*x6

2. Substitute the simplified term back into the original expression.

(4*x6*z5)/(2*z9)

3. Simplify the coefficients by dividing 4 by 2

4/2=2

(2*x6*z5)/(z9)

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

z(5−9)=z(−4)

2*x6*z(−4)

5. Rewrite with positive exponents by moving z(−4) to the denominator.

(2*x6)/(z4)

Final Answer

((2*x3)2*z5)/(2*z9)=(2*x6)/(z4)

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