Question

Which expression is equivalent to ^4 sqrt 144a^12 b^3

Answer 1

Answer:

$2a^3\sqrt[4]{9b^3}$

Step-by-step explanation:

$\sqrt[4]{144a^{12}b^3}$

144 can be written as 12*12= 2*2*3*2*2*3= 2^4 * 3^2

$\sqrt[4]{144}=\sqrt[4]{2^4*3^2}=2\sqrt[4]{9}$

$\sqrt[4]{a^{12}}=a^3$ because 12/4 = 3

$\sqrt[4]{b^3}$, we cannot simplify this because exponent 3 is less than radical 4

now we combine all the terms we simplifies

$2\sqrt[4]{9}*a^3*\sqrt[4]{b^3}$

$2a^3\sqrt[4]{9b^3}$

Answer 2

The expression equivalent to  ^4 sqrt 144a^12 b^3 will be found by simplifying our expression as follows:
 ^4 sqrt 144a^12 b^3
=(144a^12b^3)^(1/4)
=(12^2a^12b^3)^(1/4)
=12^(1/4*2)a^(12*1/4)b^(3*1/4)
=12^(1/2)a^3b^(3/4)

Answer: 12^(1/2)a^3b^(3/4)