Question

Help pleaseee!!!!!!!!

Answer 1

1

Explanation:

`((2x^3y^-3)^2)/(16x^7y^-2)\\ = (x^6y^-6)/(4x^7y^-2)\\ = (y^-4)/(4x)\\ = (1)/(4xy^4)`

Value of numerator in final answer is 1 .

Answer 2

`\textsf{Simplified:} \quad (1)/(4xy^4)`

The value of the numerator is 1.

Explanation:

Given rational expression:

`(\left(2x^3y^(-3)\right)^2)/(16x^7y^(-2))`

`\textsf{Apply the exponent rule} \;\;\boxed{(a^b)^c=a^(bc)}\;\;\textsf{to the numerator:}`

`\implies (2^2x^((3\cdot2))y^((-3\cdot 2)))/(16x^7y^(-2))`

`\implies (4x^(6)y^(-6))/(16x^7y^(-2))`

Divide the numbers 4/16 = 1/4:

`\implies (x^(6)y^(-6))/(4x^7y^(-2))`

`\textsf{Apply the exponent rule} \;\;\boxed{(1)/(a^n)=a^(-n)}:`

`\implies (x^(6)y^(-6)x^(-7)y^(2))/(4)`

Collect like terms:

`\implies (x^(6)x^(-7)y^(2)y^(-6))/(4)`

`\textsf{Apply the exponent rule} \;\;\boxed{a^b \cdot a^c=a^(b+c)}:`

`\implies (x^((6-7))y^((2-6)))/(4)`

`\implies (x^(-1)y^(-4))/(4)`

`\textsf{Apply the exponent rule} \;\;\boxed{a^(-n)=(1)/(a^n)}:`

`\implies (1)/(4xy^4)`

Therefore, the value of the numerator is 1, and the value of the denominator is 4xy⁴.