Question

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

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

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

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

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

Q

Answer 1

Answer:

It’s C I took the quiz and earned 1 point for it.

Step-by-step explanation:

Answer 2

Answer:

Option 3 -  seven to the one third power all raised to the third power equals seven to the one third times three power equals seven

Step-by-step explanation:

To find : Which equation justifies why seven to the one third power equals the cube root of seven?

Solution :

Applying Power of a Power Property,

i.e. a power of a power, multiply the exponents  as

$(x^{a})^{b}=x^{a\times b}$

We have given, seven to the one third power equals the cube root of seven

i.e. $7^{\frac{1}{3}} =\sqrt[3]{7}$

$\sqrt[3]{7}=7^{\frac{1}{3}}$

Raise to the third power,

$[7^{\frac{1}{3}}]^3$

Applying the property ,

$7^{\frac{3}{3}}=7^{1}= 7$

i.e. seven to the one third power all raised to the third power equals seven to the one third times three power equals seven.

Therefore, Option 3 is correct.