Start by distributing the exponent to each of the terms in [tex](2u)^{3}[/tex]. This will become [tex]2^{3} u^{3}[/tex], and [tex]2^{3} =8[/tex]. Now, the expression is:
[tex]\frac{2u^{3} v^{2} }{8u^{3} * u^{2} }[/tex].
We can now simplify the bottom to read: [tex]8u^{5}[/tex] because when multiplying variables raised to an exponent, we add the exponents. The expression now looks like:
[tex]\frac{2u^{3} v^{2} }{8u^{5} }[/tex]
The 2/8 simplifies to 1/4:
[tex]\frac{u^{3} v^{2} }{4u^{5} }[/tex]
Now, we have two u terms on the top and bottom. When dividing variables raised to an exponent, we subtract the exponents. However, since 3-5=-2, the term will be on the bottom to avoid the negative exponent. The final answer is:
[tex]\frac{v^{2} }{4u^{2} }[/tex]
Hope this makes sense!!
