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

Answer 1

Im not sure on this problem

Answer 2

it's using the multiplicative exponent rule

\[(a^{1/b})^{b}= (a^{(1/b)*b)})=a^{1}\]

in this case, your a value is 7 and your (1/b) value is 1/3

Answer 3

So is it seven to the one third power all raised to the third power equals seven to the one third minus three power equals seven ??

Answer 4

be careful, there's only multiplication involved

if we take the previous statement and replace a with 7 and b with 3 it should be clearer

\[(7^{1/3})^{3}= (7^{(1/3)*3)})=7^{1}\]