Answer:
[tex]\dfrac{a^6}{144b^8}[/tex]
Step-by-step explanation:
a) They did not use the exponent rule: [tex](a \cdot b)^n=a^nb^n[/tex] correctly.
They added the exponents rather than multiplied them.
b) Correct solution:
[tex](12a^{-3}b^4)^{-2}[/tex]
Apply exponent rule: [tex]a^{-b}=\dfrac{1}{a^b}[/tex]
[tex]\implies \dfrac{1}{(12a^{-3}b^4)^2}[/tex]
Apply exponent rule: [tex](a \cdot b)^n=a^nb^n[/tex]
[tex]\implies \dfrac{1}{12^2a^{(-3\times2)}b^{(4 \times2)}}[/tex]
[tex]\implies \dfrac{1}{144a^{-6}b^8}[/tex]
Apply exponent rule: [tex]\dfrac{1}{a^{-b}}=a^b[/tex]
[tex]\implies \dfrac{a^6}{144b^8}[/tex]
