Problem 21 Simplify. $$\left(-\frac{10}{3... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 4: Problem 21

Simplify. $$\left(-\frac{10}{3} \cdot \frac{3}{100}\right)^{3}$$

Short Answer

Expert verified

-\frac{1}{1000}

Step by step solution

Multiply the Fractions Inside the Parentheses

First, multiply the two fractions inside the parentheses. Multiply the numerators together and the denominators together: $ -\frac{10}{3} \cdot \frac{3}{100} = -\frac{10 \times 3}{3 \times 100} $.

Simplify the Fraction

Next, simplify the fraction obtained in Step 1. The numerator is $10 \times 3 = 30$, and the denominator is $3 \times 100 = 300$. So, $ -\frac{30}{300} = -\frac{1}{10} $.

Apply the Cube Operation

Now, take the result from Step 2 and raise it to the power of 3: $ \left(-\frac{1}{10}\right)^3 $.

Simplify the Cubed Fraction

Cube both the numerator and the denominator: $ \left(-1\right)^3 = -1 $ and $ 10^3 = 1000 $. So, $ \left(-\frac{1}{10}\right)^3 = -\frac{1^3}{10^3} = -\frac{1}{1000} $.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiplying fractions

To multiply fractions, follow a straightforward procedure. Simply multiply the numerators (top numbers) together and the denominators (bottom numbers) together. For example, if you have $ \frac{a}{b} $ and $ \frac{c}{d} $, the result is $ \frac{a \times c}{b \times d} $.

In the given problem, we have $ -\frac{10}{3} $ multiplied by $ \frac{3}{100} $. First, multiply the numerators: $ -10 \times 3 = -30 $. Next, multiply the denominators: $ 3 \times 100 = 300 $. So, the product is $ -\frac{30}{300} $.

simplifying fractions

Simplifying fractions involves reducing a fraction to its simplest form, where the numerator and denominator have no common factors other than 1. To simplify, divide both the numerator and the denominator by their greatest common divisor (GCD).

In our case, the fraction $ -\frac{30}{300} $ simplifies as follows:

Identify the GCD of 30 and 300, which is 30.
Divide both the numerator and the denominator by 30: $ \frac{-30 \text{ 梅 } 30}{300 \text{ 梅 } 30} = -\frac{1}{10} $.

Therefore, $ -\frac{30}{300} $ simplifies to $ -\frac{1}{10} $.

exponentiation of fractions

Exponentiating a fraction involves raising both the numerator and the denominator to the given power. This means if you have $ \frac{a}{b} \bigg)^n $, it becomes $ \frac{a^n}{b^n} $.

In the problem, we need to cube $ -\frac{1}{10} $. Here is how it works:

Cube the numerator: $ (-1)^3 = -1 $.
Cube the denominator: $ 10^3 = 1000 $.

Thus, $ \bigg(-\frac{1}{10}\bigg)^3 = -\frac{1}{1000} $.

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91影视

Simplify. $$\left(-\frac{10}{3} \cdot \frac{3}{100}\right)^{3}$$

Short Answer

Step by step solution

Multiply the Fractions Inside the Parentheses

Simplify the Fraction

Apply the Cube Operation

Simplify the Cubed Fraction

Key Concepts

multiplying fractions

simplifying fractions

exponentiation of fractions

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