Answer:
[tex]=-3tv^2[/tex]
Step-by-step explanation:
So we have the expression:
[tex]\sqrt[3]{3t^4v^2}\sqrt[3]{-9t^{-1}v^4}[/tex]
To simplify, combine the two radicals. Since they have the same index, we can combine them. Thus:
[tex]=\sqrt[3]{(3t^4v^2)(-9t^{-1}v^4)}[/tex]
Combine like terms:
[tex]=\sqrt[3]{(3\cdot -9)(t^4\cdot t^{-1})(v^2\cdot v^4)}[/tex]
Multiply. When multiplying the exponents, simply add the exponents:
[tex]=\sqrt[3]{-27t^3v^6}[/tex]
Now, simplify. Note that -27 can be written as (-3)^3. t^3 can be written as (t)^3 and v^6 can be written as (v^2)^3. Thus:
[tex]=\sqrt[3]{(-3)^3(t)^3(z^2)^3}[/tex]
Combine them all under one exponent:
[tex]=\sqrt[3]{(-3tv^2)^3}[/tex]
Cancel out the cube root:
[tex]=-3tv^2[/tex]
And this is the simplest it can get.
And we are done :)
Edit: Typo
