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Chapter 0: Problem 10

Evaluate the expressions. $$ \left(\frac{-2}{3}\right)^{-2} $$

Short Answer

Expert verified
The short answer is: \(\left(\frac{-2}{3}\right)^{-2} = \left(\frac{3}{-2}\right)^{2} = \frac{9}{4}\).

Step by step solution

01

Evaluate the negative exponent

Recall that a number raised to the power of a negative exponent is equal to the reciprocal of the number raised to the positive exponent: $$ \left(a^{-n}\right) = \frac{1}{a^n} $$ Using this rule, we find the reciprocal of the fraction and raise it to the power of 2: $$ \left(\frac{-2}{3}\right)^{-2} = \left(\frac{3}{-2}\right)^{2} $$
02

Simplify the expression

Now, raise the fraction to the power of 2 by squaring both the numerator and the denominator: $$ \left(\frac{3}{-2}\right)^{2} = \frac{3^2}{(-2)^2} $$ Then compute the squares of 3 and -2: $$ \frac{3^2}{(-2)^2} = \frac{9}{4} $$ The final result is \(\frac{9}{4}\).

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Most popular questions from this chapter

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(-\frac{1}{2} x^{2}-\frac{1}{2} x+1=0\)

Find all possible real solutions of each equation \(3 x^{6}-x^{4}-12 x^{2}+4=0\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(4+\frac{5}{9}\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(2 x^{2}-5=0\)

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(-\left(\frac{8(1-4)^{2}}{-9(5-1)^{2}}\right)\)
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