Question - Solving Cube Root of 81x^10y^8
Solution:
The expression in the image is the cube root of $$(81x^{10}y^8)$$, which can be written as $$(81x^{10}y^8)^{\frac{1}{3}}$$.To simplify this expression, we take the cube root of each factor separately:1. The cube root of 81, which is $$3^4$$, is 3, because $$3^3 = 27$$ and $$3^3 \times 3 = 81$$.2. The cube root of $$x^{10}$$ can be simplified by dividing the exponent by 3. This gives us $$x^{\frac{10}{3}}$$ or $$x^3 \times x^{\frac{1}{3}}$$.3. The cube root of $$y^8$$ can be simplified by dividing the exponent by 3. This gives us $$y^{\frac{8}{3}}$$ or $$y^2 \times y^{\frac{2}{3}}$$.Putting it all together, you get:$$3x^3x^{\frac{1}{3}}y^2y^{\frac{2}{3}}$$You can also leave it as $$3x^{\frac{10}{3}}y^{\frac{8}{3}}$$ if you prefer. Both forms are mathematically equivalent.
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