Evaluate: (-(3)/(2))^(4)=

Identify Base and Exponent: Identify the base and the exponent in the expression. The base is -(3/2) and the exponent is 4. This means we will multiply -(3/2) by itself 4 times.Recognize Even Exponent: Recognize that an even exponent will result in a positive number. Since the exponent is 4, which is an even number, the result of raising any real number to the 4th power will be positive, regardless of whether the base is positive or negative.Calculate Absolute Value: Calculate the absolute value of the base raised to the power of 4. (3/2)^4 = (3/2) * (3/2) * (3/2) * (3/2)Multiply Fractions: Multiply the fractions. (3/2) * (3/2) = 9/4 and (3/2) * (3/2) = 9/4, so now we have (9/4) * (9/4).Multiply Results: Multiply the results from Step 4. (9/4) * (9/4) = 81/16Final Result: Since the original base was negative and the exponent is even, the final result will be positive. Therefore, (-(3/2))^4 = 81/16.

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Evaluate: $\newline$ $(-\frac{3}{2})^{4}=$

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Q. Evaluate:

\newline

(-\frac{3}{2})^{4}=

Identify Base and Exponent: Identify the base and the exponent in the expression. $\newline$ The base is $-\left(\frac{3}{2}\right)$ and the exponent is $4$ . This means we will multiply $-\left(\frac{3}{2}\right)$ by itself $4$ times.
Recognize Even Exponent: Recognize that an even exponent will result in a positive number. Since the exponent is $4$ , which is an even number, the result of raising any real number to the $4$ th power will be positive, regardless of whether the base is positive or negative.
Calculate Absolute Value: Calculate the absolute value of the base raised to the power of $4$ . $\newline$ $\left(\frac{3}{2}\right)^4 = \left(\frac{3}{2}\right) * \left(\frac{3}{2}\right) * \left(\frac{3}{2}\right) * \left(\frac{3}{2}\right)$
Multiply Fractions: Multiply the fractions. $\newline$ $(\frac{3}{2}) \times (\frac{3}{2}) = \frac{9}{4}$ and $(\frac{3}{2}) \times (\frac{3}{2}) = \frac{9}{4}$ , so now we have $(\frac{9}{4}) \times (\frac{9}{4})$ .
Multiply Results: Multiply the results from Step $4$ . $\newline$ $(\frac{9}{4}) \times (\frac{9}{4}) = \frac{81}{16}$
Final Result: Since the original base was negative and the exponent is even, the final result will be positive. $\newline$ Therefore, $(-\left(\frac{3}{2}\right))^4 = \frac{81}{16}$ .