Answer :
Answer:
Part 1) [tex]a=-\frac{1}{4c^6}[/tex]
Part 2) [tex]a=-\frac{1}{4c^{-6}}[/tex]
Step-by-step explanation:
Part 1) we have
[tex]a=2b^{3}[/tex] ----> equation A
[tex]b=-\frac{1}{2}c^{-2}[/tex] ----> equation B
substitute equation B in equation A
[tex]a=2(-\frac{1}{2}c^{-2})^{3}[/tex]
Applying property of exponents
[tex](x^{m})^{n}=x^{m*n}[/tex]
[tex]x^{-m} =\frac{1}{x^{m}}[/tex]
[tex]a=2(-\frac{1}{2}c^{-2})^{3}=2(-\frac{1}{2})^3(c^{-2})^{3}=2(-\frac{1}{8})(c^{-6})=-\frac{1}{4c^6}[/tex]
therefore
[tex]a=-\frac{1}{4c^6}[/tex]
Part 2) we have
[tex]a=2b^{3}[/tex] ----> equation A
[tex]b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2}[/tex] ----> equation B
substitute equation B in equation A
[tex]a=2(-\frac{c^{2}}{2})^{3}[/tex]
Applying property of exponents
[tex](x^{m})^{n}=x^{m*n}[/tex]
[tex]x^{-m} =\frac{1}{x^{m}}[/tex]
[tex]a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})[/tex]
simplify
[tex]a=-\frac{c^{6}}{4}[/tex]
therefore
[tex]a=-\frac{1}{4c^{-6}}[/tex]