Question

Plz write this on paper help me and send it❤️

Answer 1

1.
`27^{(2)/(3) } =9`

2.
`\sqrt{36^(3) } =216`

3.
`(-243)^{(3)/(5) } =-27`

4.
`40^{(2)/(3)}=4\sqrt[3]{25} =4325`

5. Step 4:
`((343)/(27)) ^(-1) =(27)/(343)`

6.
`D. -72cd^(7)`

Explanation:

Use the following properties:

`a^{(x)/(y) } =\sqrt[x]{a^(y) }`

`\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}`

`a^(-n) =(1)/(a^(n) )`

`(xy)^(z) =x^(z) y^(z) \\\\`

`(x^(y)) ^(z) =x^(yz)`

`x^(y) x^(z) =x^(y+z)`

So:

1.
`27^{(2)/(3) } =\sqrt[3]{27^(2)} =\sqrt[3]{729} }=9`

2.
`\sqrt{36^(3) } =√(36*36*36) =√(36) √(36) √(36) =6*6*6=216`

3.
`(-243)^{(3)/(5) } =\sqrt[5]{-243^(3) } =\sqrt[5]{-14348907} =-27`

4.
`40^{(2)/(3)}=\sqrt[3]{40^(2) } =\sqrt[3]{2^(6) 5^(2) } =\sqrt[3]{2^(6) } \sqrt[3]{5^(2) } =2^{(6)/(3) } 5^{(2)/(3) } =4 *5^{(2)/(3) } =4\sqrt[3]{5^(2) } =4\sqrt[3]{25}=4325`

5.
`((343)/(27)) ^(-1) =(1)/((343)/(27) ) =(27)/(343)`

6.

`(-8c^(9) d^(-3) )^{(1)/(3) } *(6c^(-1)d^(4))^(2) =\sqrt[3]{-8} c^(3) d^(-1) 36c^(-2) d^(8) \\\\-2c^(3) d^(-1) 36c^(-2) d^(8)=-72cd^(7)`