Question

If a=2b^3 and b= -1/2c ^-2,express a in terms of c.

Answer 1

Part 1)
`a=-(1)/(4c^6)`

Part 2)
`a=-(1)/(4c^(-6))`

Explanation:

Part 1) we have

`a=2b^(3)` ----> equation A

`b=-(1)/(2)c^(-2)` ----> equation B

substitute equation B in equation A

`a=2(-(1)/(2)c^(-2))^(3)`

Applying property of exponents

`(x^(m))^(n)=x^(m*n)`

`x^(-m) =(1)/(x^(m))`

`a=2(-(1)/(2)c^(-2))^(3)=2(-(1)/(2))^3(c^(-2))^(3)=2(-(1)/(8))(c^(-6))=-(1)/(4c^6)`

therefore

`a=-(1)/(4c^6)`

Part 2) we have

`a=2b^(3)` ----> equation A

`b=-(1)/(2c^(-2))=-(c^(2))/(2)` ----> equation B

substitute equation B in equation A

`a=2(-(c^(2))/(2))^(3)`

Applying property of exponents

`(x^(m))^(n)=x^(m*n)`

`x^(-m) =(1)/(x^(m))`

`a=2(-(c^(2))/(2))^(3)=2(-(c^(6))/(8))`

simplify

`a=-(c^(6))/(4)`

therefore

`a=-(1)/(4c^(-6))`