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FromTheMoon [43]
3 years ago
6

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

Mathematics
1 answer:
ElenaW [278]3 years ago
6 0

Answer:

Part 1) a=-\frac{1}{4c^6}

Part 2) a=-\frac{1}{4c^{-6}}

Step-by-step explanation:

Part 1) we have

a=2b^{3} ----> equation A

b=-\frac{1}{2}c^{-2} ----> equation B

substitute equation B in equation A

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

Applying property of exponents

(x^{m})^{n}=x^{m*n}

x^{-m} =\frac{1}{x^{m}}

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}

therefore

a=-\frac{1}{4c^6}

Part 2) we have

a=2b^{3} ----> equation A

b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2} ----> equation B

substitute equation B in equation A

a=2(-\frac{c^{2}}{2})^{3}

Applying property of exponents

(x^{m})^{n}=x^{m*n}

x^{-m} =\frac{1}{x^{m}}

a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})

simplify

a=-\frac{c^{6}}{4}

therefore

a=-\frac{1}{4c^{-6}}

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