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Chapter 2: Problem 36

Simplify. \(\left(-\frac{7 a^{4} b}{8 c^{6}}\right)^{2}\)

Short Answer

Expert verified
The simplified term is \(\frac{49 a^{8} b^{2}}{64 c^{12}}\).

Step by step solution

01

Identify each part of the term

We have a numeric part (-7/8) raised to the power of 4, and variables a, b, and c with their respective exponents.
02

Apply the power rule to the numeric part

(-7/8)^2 = (-7)^2 / (8)^2 = 49 / 64
03

Apply the power rule to the variables

Raise each variable to the power of 2: (a^4)^2 = a^(4*2) = a^8, (b)^2 = b^2, and (c^6)^2 = c^(6*2) = c^12.
04

Combine the results

Multiply the simplified numeric part with the simplified variables: (49/64) * a^8 * b^2 / c^12.
05

Write the final answer

The simplified term is \(\frac{49 a^{8} b^{2}}{64 c^{12}}\).

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