Answer:
a) [tex]w^{13} x^{5} y^{6}[/tex]
b) [tex]\frac{x}{3y^{6} }[/tex]
Step-by-step explanation:
a) [tex](w^{2} xy^{3} )^{2}(w^{3}x )^{3}[/tex]
1. Distribute the second power (2) outside the first pair of parenthesis:
[tex](w^{2(2)} x^{2} y^{3(2)} )[/tex]
= [tex]w^{4} x^{2} y^{6} (w^{3}x )^{3}[/tex]
2. Distribute the third power (3) outside the second pair of parenthesis:
[tex](w^{3(3)} x^{3} )[/tex]
= [tex]w^{4} x^{2} y^{6} w^{9} x^{3}[/tex]
3. Combine like terms:
[tex]w^{13} x^{5} y^{6}[/tex]
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b) [tex]\frac{2x^{2} y^{5} }{6xy^{11} }[/tex]
1. Factor the number 6 (= 2 · 3):
[tex]\frac{2x^{2} y^{5} }{2(3)xy^{11} }[/tex]
2. Cancel the common factor (2):
[tex]\frac{x^{2} y^{5} }{3xy^{11} }[/tex]
3. Cancel out [tex]xy^{5}[/tex] in the numerator an denominator:
[tex]\frac{x}{3y^{6} }[/tex]
hope this helps!