Simplify $a^{-7}/(ab^{6}) + (1/a^{3})^{-2}$ .

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Worked solution

1. Simplify the first term using index laws for division.

$\frac{a^{-7}}{ab^{6}}=\frac{a^{-7}}{a^1b^6}=a^{-7-1}b^{-6}=a^{-8}b^{-6}=\frac{1}{a^8b^6}$

2. Simplify the second term using the power of a quotient and negative index laws.

$(\frac{1}{a^3})^{-2}=(a^{-3})^{-2}=a^{6}$

3. Add the two simplified terms using a common denominator.

$\frac{1}{a^8b^6}+a^6=\frac{1}{a^8b^6}+\frac{a^6(a^8b^6)}{a^8b^6}=\frac{1+a^{14}b^6}{a^8b^6}$

Answer

$\dfrac{a^{6}b^{6}+1}{a^{8}b^{6}}$

AI analysis — may contain mistakes.

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