Question

100 POINTS!!!

Which expression is equivalent to RootIndex 4 StartRoot 144 a Superscript 12 Baseline b cubed EndRoot? Assume a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0. 2 a cubed (RootIndex 4 StartRoot 9 b cubed EndRoot) 2 a Superscript 4 Baseline b (RootIndex 4 StartRoot 18 EndRoot) 6 a cubed (RootIndex 4 StartRoot 3 b cubed EndRoot) 12 a Superscript 6 Baseline b (RootIndex 4 StartRoot b EndRoot)

Answer 1

The Answer is A

Step-by-step explanation

2 a cubed (RootIndex 4 StartRoot 9 b cubed EndRoot)

Answer 2

2 a^3 b ^3/4 * 3^1/2

2 a^3 b ^3/4 9^ 1/4

Explanation:

(144 a^12 b^3) ^ (1/4)

Rewriting

12 ^2 ^1/4 a^12^1/4 b^3^1/4

We know a^b^c = a^ (b*c)

12 ^ 1/2 a^3 b^3/4

(4*3) ^ 1/2 a^3 b^3/4

We know (ab)^c = a^c * b^c

4^1/2 * 3^1/2

2 a^3 b ^3/4 * 3^1/2

Rewriting 3 as 9 ^ 1/4

2 a^3 b ^3/4 9^ 1/4