Question

What is the simplest radical form of the expression?

(8x^7y^4)^2/3

Answer 1

Expand
`\bf{(8x^(7)y^(4))^{(2)/(3) } }`

`\bf{8^{(2)/(3) }(x^(7))^{(2)/(3) }(y^(4))^{(2)/(3) } }`

To raise a power to another power, multiply the exponents. Multiply 7 and 2/3 to get 14/3.

`\bf{8^{(2)/(3)}x^{(14)/(3) }(y^(4))^{(2)/(3) } }`

To raise a power to another power, multiply the exponents. Multiply 4 and 2/3 to get 8/3.

`\bf{8^{(2)/(3)}x^{(14)/(3) }y^{(8)/(3) } }`

Calculate 8 to the power of 2/3 and you get 2/4.

`\bf{4x^{(13)/(4) }y^{(8)/(3) } \ \ ==== > \ \ \ Answer }`

Answer 2

`\large \text{$ 4 x^{(14)/(3)}y^{(8)/(3)}$}`

Explanation:

Given expression:

`(8x^7y^4)^{(2)/(3)}`

`\textsf{Apply exponent rule} \quad (a \cdot b)^c=a^(c) \cdot b^(c):`

`\implies 8^{(2)/(3)} \cdot (x^7)^{(2)/(3)}\cdot(y^4)^{(2)/(3)}`

`\implies 4 \cdot (x^7)^{(2)/(3)}\cdot(y^4)^{(2)/(3)}`

`\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):`

`\implies 4 \cdot x^{(14)/(3)}\cdot y^{(8)/(3)}`

`\implies 4 x^{(14)/(3)}y^{(8)/(3)}`