Solving Cube Root of 81x^10y^8
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.
