Question

Which equation justifies why nine to the one third power equals the cube root of nine?

nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine

nine to the one third power all raised to the third power equals nine raised to the one third plus three power equals nine

nine to the one third power all raised to the third power equals nine raised to the one third minus three power equals nine

nine to the one third power all raised to the third power equals nine raised to the three minus one third power equals nine

Answer 1

Option 1.

Explanation:

The given equation is

`9^{(1)/(3)}=\sqrt[3]{9}`

We need to find the equation which justifies the given equation.

Taking cube on both sides.

`(9^{(1)/(3)})^3=(\sqrt[3]{9})^3`

`(9^{(1)/(3)})^3=9`

Taking LHS,

`LHS=(9^{(1)/(3)})^3`

Using power property of exponents.

`LHS=9^{(1)/(3)* 3}`
`[\because (a^m)^n=a^(mn)]`

`LHS=9^{(3)/(3)}`

`LHS=9^(1)`

`LHS=9`

`LHS=RHS`

The required equation is

`(9^{(1)/(3)})^3=9^{(1)/(3)* 3}=9`

"Nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine".

Therefore, the correct option is 1.

Answer 2

nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine

Explanation:

we know that

The Power of a Power Property , states that :To find a power of a power, multiply the exponents

so

`(a^(b))^(c)=a^(b*c)`

In this problem we have

`9^{(1)/(3)} =\sqrt[3]{9}`

Remember that

`\sqrt[3]{9}=9^{(1)/(3)}`

Raise to the third power

`[9^{(1)/(3)}]^3`

Applying the power of power property

`9^{(3)/(3)}`

`9^(1)`

`9`

therefore

nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine