the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to…

Explanation:

Step1: Identify decay formula

The formula for radioactive - decay is $A = A_0\times(\frac{1}{2})^n$, where $A_0$ is the initial amount, $n$ is the number of half - lives, and $A$ is the final amount.

Step2: Substitute values

Given $A_0 = 180$ grams and $n = 5$. Substitute these values into the formula: $A=180\times(\frac{1}{2})^5$.

Step3: Calculate $(\frac{1}{2})^5$

$(\frac{1}{2})^5=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{32}$.

Step4: Calculate final amount

$A = 180\times\frac{1}{32}=\frac{180}{32}= 5.625$ grams.

Step5: Round the answer

Rounding $5.625$ to the nearest gram gives $6$ grams.

Answer:

6 grams