Question

question 5
simplify $sqrt6{b^{6}}$. assume that $b > 0$.
score: 4/21 answered: 4/21
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work 11: evaluating roots (ck 2.1)

Explanation:

Step1: Recall root - exponent relationship

We know that $\sqrt[n]{a}=a^{\frac{1}{n}}$. So, $\sqrt[6]{b^{6}}=(b^{6})^{\frac{1}{6}}$.

Step2: Apply power - of - a - power rule

According to the power - of - a - power rule $(a^{m})^{n}=a^{mn}$. Here, $m = 6$ and $n=\frac{1}{6}$, so $(b^{6})^{\frac{1}{6}}=b^{6\times\frac{1}{6}}$.

Step3: Calculate the exponent

$6\times\frac{1}{6}=1$, so $b^{6\times\frac{1}{6}} = b^{1}=b$.

Answer:

$b$