Questions: (5.0 g^2) · (9.0 g)=?

(5.0 g^2) · (9.0 g)=?

Transcript text: $\left(5.0 \mathrm{~g}^{2}\right) \cdot(9.0 \mathrm{~g})=?$

Solution

Solution Steps

To solve the given expression \((5.0 \, \text{g}^2) \cdot (9.0 \, \text{g})\), we need to multiply the coefficients and add the exponents of the like terms. Here, we multiply the numerical coefficients 5.0 and 9.0, and since we are multiplying terms with the same base (g), we add the exponents (2 and 1).

Step 1: Identify the Expression Components

The given expression is \((5.0 \, \text{g}^2) \cdot (9.0 \, \text{g})\). It consists of two parts: the coefficients \(5.0\) and \(9.0\), and the variable \(g\) with exponents \(2\) and \(1\).

Step 2: Multiply the Coefficients

Multiply the numerical coefficients: \[ 5.0 \times 9.0 = 45.0 \]

Step 3: Add the Exponents

Since the base \(g\) is the same, add the exponents: \[ 2 + 1 = 3 \]

Final Answer

Combine the results to express the final product: \[ \boxed{45.0 \, \text{g}^3} \]

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Snoring has long been considered an irritating but benign habit. However, "even isolated snoring might not be harmless," according to new research reported in the Forbes article "Snoring: A New Tip-Off to Stroke" (Haiken). The American Academy of Head and Neck Surgery defines snoring as "what you hear as a result of a form of blockage that obstructs the flow of air through the mouth or nose. The blockage causes the tissues of the airway to vibrate and flap." However, it is not the vibration and flapping of airway tissues that makes Henry Ford Hospital researchers Robert Deeb, MD, and Karen Yaremchuk, MD, so concerned. "Snoring can reveal damage to the carotid arteries-the arteries that supply oxygen-rich blood to the brain." In their study, Deeb and Yaremchuk found that the damage to the carotid arteries could be due to the trauma and inflammation caused by the vibrations of snoring. Deeb said that snorers should seek treatment since they could be at risk for coronary artery diseases. Deeb said, "Patients need to seek treatment in the same way they would if they had sleep apnea, high blood pressure or other risk factors for cardiovascular disease." Early detection of cardiovascular disease indicated by snoring can lead people toward an earlier diagnosis and treatment of heart disease. Deeb said, "Snoring is generally regarded as a cosmetic issue by health insurance, requiring significant out-of-pocket expenses by patients. We're hoping to change that thinking so patients can get the early treatment they need, before more serious health issues arise" (Haiken). Sources: "Don't Ignore the Snore: Snoring May Be Early Sign of Future Health Risks." Science Daily, 24 Jan. 2013, www.sciencedaily.com/releases/2013/01/130124122741.htm; Haiken, Melanie. "Snoring: A New Tip-Off to Stroke and Heart Disease." Forbes, 28 Jan. 2013, www.forbes.com/sites/melaniehaiken/2013/01/28/snoring-is-a-tip-off-to-stroke-and-heart-disease-new-research-shows/#f5a21ea56c19.

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