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Chapter 0: Problem 113

Use the order of operations to simplify each expression. $$\frac{5 \cdot 2-3^{2}}{\left[3^{2}-(-2)\right]^{2}}$$

Short Answer

Expert verified
The simplified resulting value of the expression is \(\frac{1}{121}\)

Step by step solution

01

Apply the indices

Before dealing with any other operations, indices (exponents) should be dealt with first. Hence, replace \(3^{2}\) with 9 in both numerator and denominator. We now have: \[\frac{5 \cdot 2-9}{(9-(-2))^{2}}\]
02

Execution of multiplication in the numerator and addition in the denominator

We need to perform the multiplication operation in the numerator and the addition operation in the denominator before subtraction: \[\frac{10-9}{(9+2)^{2}} = \frac{1}{11^{2}} \]
03

Apply exponent in the denominator

Next, apply the exponent in the denominator: \[\frac{1}{121} \]

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Most popular questions from this chapter

$$\text { Factor completely.}$$ $$(x-y)^{4}-4(x-y)^{2}$$

Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$\frac{x^{2}+6 x+5}{x^{2}-25}$$

Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

Find the intersection of the sets. $$\\{1,3,5,7\\} \cap\\{2,4,6,8,10\\}$$

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\\{-7,-0 . \overline{6}, 0, \sqrt{49}, \sqrt{50}\\}$$
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