Question

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

Answer 1

For this case we must find the justification of:

$10 ^ {\frac {1} {3}} = \sqrt [3] {10}$

By definition of properties of powers and roots we have to meet:

$a ^ {\frac {m} {n}} = \sqrt [n] {a ^ m}$

So, if we have:

$\sqrt [3] {10} = \ \sqrt [3] {10 ^ 1} = 10 ^ {\frac {1} {3}}$

Other property states that:

$(a ^ n) ^ m = a ^ {n * m}$

So, the expression: "Ten to the one third power all raised to the third power" is represented as:

$(10 ^{\frac {1} {3}}) ^ 3 = 10 ^ {\frac {3*1} {3}} = 10 ^ 1 = 10$

ANswer;

Option B

Answer 2

Answer: The answer would be (10^1/3)³ = 10 ^(1/3×3) =10

Step-by-step explanation:

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