Question

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

Answer 1

Answer:

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

Step-by-step 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

$9^{\frac{1}{3}} =\sqrt[3]{9}$

Remember that

$\sqrt[3]{9}=9^{\frac{1}{3}}$

Raise to the third power

$[9^{\frac{1}{3}}]^3$

Applying the power of power property

$9^{\frac{3}{3}}$

$9^{1}$

$9$

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

Answer 2

Answer:

Option 1.

Step-by-step explanation:

The given equation is

$9^{\frac{1}{3}}=\sqrt[3]{9}$

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

Taking cube on both sides.

$(9^{\frac{1}{3}})^3=(\sqrt[3]{9})^3$

$(9^{\frac{1}{3}})^3=9$

Taking LHS,

$LHS=(9^{\frac{1}{3}})^3$

Using power property of exponents.

$LHS=9^{\frac{1}{3}\times 3}$           $[\because (a^m)^n=a^{mn}]$

$LHS=9^{\frac{3}{3}}$

$LHS=9^{1}$

$LHS=9$

$LHS=RHS$

The required equation is

$(9^{\frac{1}{3}})^3=9^{\frac{1}{3}\times 3}=9$

"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.