Question

simplify and rewrite only as positive exponents:

x^14x^-9y^19z^-3 / (x^-2)^4x-^-9y^22

Answer 1

\[x ^{14}x ^{-9}y ^{19}z ^{-3} \div \left( x ^{-2} \right)^{4}x -9y ^{22}\]

Answer 2

x^14 * x^-9 * y^-19 * z^-3 / (x^-2)^4 * x^-9 * y^22

1) let's simplify (x^-2)^4 as x^-8
2) use the relationship " (1/(x^2))=(x^-2)" to rewrite terms in denominator as numerator terms
x^14 * x^-9 * y^-19 * z^-3 / x^-8 * x^-9 * y^22 becomes
x^14 * x^-9 * y^-19 * z^-3 * (x^8 * x^9 * y^-22)
3) now combine like terms
x^(14-9+8+9) * y^(-19-22) * z^(-3)
x^22 * y^-41 * z^-3
4) now rewrite using relationship shown in step 2):
x^22 / y^41 * z^3
This is your solution.