The answer is:[tex]4x^2y^6[/tex]
Step-by-step explanation:
Given expression is;
[tex]\sqrt[3]{(8x^3y^9)^2}[/tex]
We have to simplify the expression to see if the answer is correct
First of all, the exponent in the cube root will be solved, so
[tex]=\sqrt[3]{(8)^2x^{(3*2)}y^{(9*2)}} \\=\sqrt[3]{64x^6y^{18}}[/tex]
Now solving the cube root
[tex]({64x^6y^{18}})^{\frac{1}{3}}\\={(64)^{\frac{1}{3}}*x^{(6*\frac{1}{3})}y^{(18*\frac{1}{3})}}\\=(4^3)^{\frac{1}{3}} * x^2 * y^6\\=4x^2y^6[/tex]
Hence,
The answer is:[tex]4x^2y^6[/tex]
Keywords: Exponents, cube roots
Learn more about exponents at:
- brainly.com/question/10435836
- brainly.com/question/10541435
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