Final answer:
To express the multiplication of 3B to the 1/2 power by B to the 4/3 power in radical form, add the exponents and write as a single term under a radical: 3 times the sixth root of B to the 11th power, or 3 times the cube root of B squared times B.
Step-by-step explanation:
The student is asking how to write the expression 3B raised to the 1/2 power times B raised to the power of 4/3 in radical form. When dealing with exponents, there are some basic rules that must be followed. By using the rule that when you multiply exponential terms with the same base, you add the exponents, we can combine the two expressions. In arithmetic form, the expression is:
3B1/2 × B4/3
We treat the numerical coefficient ('3') separately and multiply the exponents of 'B':
3 × B1/2 + 4/3
To add the exponents of 'B', we find a common denominator, which in this case would be 6, and then add:
3 × B3/6 + 8/6 = 3 × B11/6
This can be written in radical form as:
3 × the sixth root of B11
or, alternatively:
3 × the cube root of B2 times B
since taking the sixth root of B to the 11th power is equivalent to taking the cube root of B squared (since 2 times 3 is 6) and then multiplying by B once more (since 11 is one more than 10, which is divisible by 6).