(d) (-(1)/(2)+(1)/(3))^(2)-[(1)/(4)+(-(1)/(3))]+(-(1)/(20))

Simplify and Calculate: First, we need to simplify the expression inside the first set of parentheses. Calculate -(1/2) + (1/3).Raise to Power: Now, raise the result to the power of 2. Calculate (-1/6)^2.Simplify Inside Brackets: Next, simplify the expression inside the square brackets. Calculate 1/4 - 1/3.Combine and Subtract: Now, combine the results from the previous steps and subtract the last term. Calculate 1/36 - (-1/12) - 1/20.Find Common Denominator: Simplify the expression by finding a common denominator and combining the terms. Calculate 4/36 - 1/20.

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(d)
(-(1)/(2)+(1)/(3))^(2)-[(1)/(4)+(-(1)/(3))]+(-(1)/(20))

(d) $\left(-\frac{1}{2}+\frac{1}{3}\right)^{2}-\left[\frac{1}{4}+\left(-\frac{1}{3}\right)\right]+\left(-\frac{1}{20}\right)$

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Algebra 1

Multiplication with rational exponents

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Q. (d)

\left(-\frac{1}{2}+\frac{1}{3}\right)^{2}-\left[\frac{1}{4}+\left(-\frac{1}{3}\right)\right]+\left(-\frac{1}{20}\right)

Simplify and Calculate: First, we need to simplify the expression inside the first set of parentheses. $\newline$ Calculate $-\frac{1}{2} + \frac{1}{3}$ .
Raise to Power: Now, raise the result to the power of $2$ . Calculate $(-\frac{1}{6})^2$ .
Simplify Inside Brackets: Next, simplify the expression inside the square brackets. Calculate $\frac{1}{4} - \frac{1}{3}$ .
Combine and Subtract: Now, combine the results from the previous steps and subtract the last term. $\newline$ Calculate $\frac{1}{36} - \left(-\frac{1}{12}\right) - \frac{1}{20}.$
Find Common Denominator: Simplify the expression by finding a common denominator and combining the terms. $\newline$ Calculate $\frac{4}{36} - \frac{1}{20}.$