160 x 243 ^1/5 is equal to 38880^1/5. Find the prme factorization:
[tex]=\left(2^5\cdot \:3^5\cdot \:5\right)^{\frac{1}{5}}[/tex]
Then, follow the rule: a x b^c = a^c b^c
[tex]=5^{\frac{1}{5}}\left(2^5\right)^{\frac{1}{5}}\left(3^5\right)^{\frac{1}{5}}[/tex]
Apply the rule [tex]a^m^{\frac{1}{n}}=a^{\frac{m}{n}}[/tex]
[tex]2^5^{\frac{1}{5}}=2^{\frac{5}{5}}=2.
So far the equation should be 2\cdot \:5^{\frac{1}{5}}\left(3^5\right)^{\frac{1}{5}}.
Apply the same rule for the term \left(3^5\right)^{\frac{1}{5}}:
3^5^{\frac{1}{5}}=3^{\frac{5}{5}}=3
=2\cdot \:3\cdot \:5^{\frac{1}{5}}
Last, refine: =6\cdot \:5^{\frac{1}{5}}[/tex]
For A: the decimal form 'd be 8.27838...
For D: the decimal form'd be 6.89865...
The answer is A. The expression is equal to 8.27838... like option A.
