Question

which of the following is equal to the expression below?
(160 · 243)^{\frac{1}{5}}
a. 96
b. 6 sqrt5{5}
c. 5 sqrt5{5}
d. 80

Explanation:

Step1: Factorize the numbers inside

$160 = 2^5 \times 5$, $243 = 3^5$

Step2: Multiply the factored terms

$160 \times 243 = 2^5 \times 5 \times 3^5 = (2 \times 3)^5 \times 5 = 6^5 \times 5$

Step3: Apply the fractional exponent

$(6^5 \times 5)^{\frac{1}{5}} = (6^5)^{\frac{1}{5}} \times 5^{\frac{1}{5}}$

Step4: Simplify each term

$(6^5)^{\frac{1}{5}} = 6$, $5^{\frac{1}{5}} = \sqrt[5]{5}$

Answer:

B. $6 \sqrt[5]{5}$