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Example of Evaluating when c=- rac{1}{2} and d=- rac{4}{3}
To evaluate the expression when c=- rac{1}{2} and d=- rac{4}{3}, substitute the fractional values and evaluate the expression using the order of operations:
- Substitute: Replace the variables with their given negative fraction values using parentheses: 4\left(- rac{1}{2} ight)^3\left(- rac{4}{3} ight).
- Simplify exponents: Cube the fraction. A negative value raised to an odd power remains negative, so \left(- rac{1}{2} ight)^3 = - rac{1}{8}. The expression evaluates to 4\left(- rac{1}{8} ight)\left(- rac{4}{3} ight).
- Multiply the fractions: Combine the parts into one fraction: rac{4 \cdot (-1) \cdot (-4)}{1 \cdot 8 \cdot 3}. Since there are two negative numbers being multiplied, the result will be positive.
- Divide out common factors: The numerator becomes and the denominator . Dividing out the common factor of simplifies the expression to rac{2}{3}.
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
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Example of Evaluating when a=- rac{2}{3} and b=- rac{1}{2}
Example of Evaluating when c=- rac{1}{2} and d=- rac{4}{3}
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