Multiply x to the 1 third power times x to the 3 sevenths power. x to the 16 over 21 power x to the 2 over 21 power x to the 1 sevenths power x to the 2 fifths power

Correct answer is: x to the 16 over 21 power.

Step-by-step explanation:

Given is x to 1 third power times x to the 3 sevenths power.

i. e. x^ (1/3) times x^ (3/7)

We know the formula; a^m times a^n = a^ (m+n)

So, x^ (1/3) times x^ (3/7) = x^ (1/3 + 3/7)

Finding sum of powers; i. e. 1/3 + 3/7

Common denominator is 21. So it would be 7/21 + 9/21.

So, x^ (1/3) times x^ (3/7) = x^ (7/21 + 9/21)

x^ (1/3) times x^ (3/7) = x^ (16/21)

Hence, the correct answer is x to the 16 over 21 power.