Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### Simplify the Following Expression
#### Expression:
\[ \frac{x^5}{y^{11}} \cdot \frac{x^{-9}y^{14}z^7}{xy^0z^{22}} \cdot \frac{(xyz)^4}{x^{-8}} \]
#### Options:
1. \(\frac{x^{18}}{y^8z^9}\)
2. \(\frac{x^7y^7}{z^{11}}\)
3. \(x^9y^{16}z^2\)
4. \(\frac{1}{x^8y^7z^4}\)
#### Explanation:
This problem asks you to simplify the given mathematical expression. The correct option will be the one that correctly represents the simplified form of the given expression through a process using the laws of exponents.
Useful rules and steps to simplify include:
1. Combine the exponents of like bases by adding or subtracting them according to the multiplication and division rules.
2. Apply the power rule: \((a^m)^n = a^{mn}\).
#### Graphical Representation:
The image contains the same mathematical expression and four options inside circles representing different results from simplifying the given expression. Each form in the options utilizes varying coefficients and powers of \(x\), \(y\), and \(z\).
Understanding the structure and methods of simplifying such expressions is vital in algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F098f8e04-469a-4a6a-8094-b45e233f0633%2F74fe4cd2-7648-464f-bd26-3b9628049c91%2F1qc7xby_processed.jpeg&w=3840&q=75)
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