Question

Simplify: (x²y³z⁻³)⁷(xy⁴)

Answer 1

`\huge \boxed{ (x^(15) y^(25))/(z^(21) ) }`

Explanation:

`(x^2 y^3 z^(-3))^7 (xy^4)`

`\sf Apply \ exponent \ rule : (a^b)^c=a^(bc)`

`(x^(2 * 7) y^(3 * 7) z^(-3 * 7))(xy^4)`

`(x^(14) y^(21) z^(-21))(xy^4)`

`x^(14) * y^(21) * z^(-21) * x * y^4`

`\sf Apply \ exponent \ rule : a^b * a^c=a^(b+c)`

`x^(14) * x^1 * y^(21) * y^4 * z^(-21)`

`x^(14+1) * y^(21+4) * z^(-21)`

`x^(15) * y^(25) * z^(-21)`

`\displaystyle \sf Apply \ exponent \ rule : a^(-b) =(1)/(a^b)`

`\displaystyle x^(15) * y^(25) * (1)/(z^(21) )`

`\displaystyle (x^(15) y^(25))/(z^(21) )`

Answer 2

`\huge\boxed{(x^(15)y^(25))/(z^(21)) }`

Explanation:

`(x^2y^3z^(-3))^7(xy^4)\\`

Expanding Parenthesis

`(x^(2*7 ) y^(3*7)z^(-3*7))(xy^4)\\x^(14)y^(21)z^(-21) * xy^4`

Combining like terms

`x^(14) * x * y^(21) * y^4 * z^(-21)`

When bases are same , powers are to be added

`x^(14+1) y^(21+4) x^(-21)`

`x^(15) y^(25) z^(-21)`

Neutralizing the negative sign by shifting z to the denominator

`(x^(15)y^(25))/(z^(21))`