Answer:
[tex]\frac{x^{24} }{8y^{15}}[/tex]
Step-by-step explanation:
[tex](\frac{x^{3}y^{-2}}{2x^{-5}y^{3}})^3[/tex]
We will use
1)Product Rule
a^m ∙ a^n = a^(m + n),
this says that to multiply two exponents with the same base, you keep the base and add the powers.
2)Quotient Rule
[tex]\frac{a^{m} }{a^{n}}=a^{m-n}[/tex]
this says that to divide two exponents with the same base, you keep the base and subtract the powers.
So by considering these two laws
[tex](x^{3-(-5)}y^{-2-3}})/2 )^{3}[/tex]
[tex](\frac{x^{8}y^{-5} }{2})^{3}[/tex]
[tex](\frac{x^{8} }{2y^{5}})^{3}[/tex]
3)Power Rule (Powers to Powers)
(a^m)^n = a^(mn)
[tex]\frac{x^{24} }{8y^{15}}[/tex]
