Rotational exponents simplify \sqrt[5]{128 {a}^(8) } {b}^(10)

Question

Rotational exponents
simplify

`\sqrt[5]{128 {a}^(8) } {b}^(10)`

Answer 1

`\bf \sqrt[5]{128a^8}b^(10)\implies b^(10)\sqrt[5]{128a^8}~~ \begin{cases} 128=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^7\\ \qquad 2^(2+5)\\ \qquad 2^2 \cdot 2^5\\ a^8=a^(3+5)\\ \qquad a^3\cdot a^5 \end{cases} \\\\\\ b^(10)\sqrt[5]{2^2\cdot 2^5\cdot a^3\cdot a^5}\implies b^(10)(2)(a)\sqrt[5]{2^2a^3}\implies 2ab^(10)\sqrt[5]{4a^3}`

Answer 2

Hi!

If you were to simplify this expression you would get
`2a b^(10) \sqrt[5]{4 a^(3) }`