Power in mathematics refers to the number of times a number is multiplied by itself. It is denoted using the exponent notation.

The exponent notation is written as a superscript to the right of the base number. For example, in the expression 3^{4}, 3 is the base and 4 is the exponent. This means 3 is multiplied by itself 4 times.

To calculate a power, multiply the base number by itself the number of times indicated by the exponent. For example, 2^{3} is equal to 2 * 2 * 2, which equals 8.

There are a few properties of powers that are important to understand:

**Product of Powers:**When multiplying powers with the same base, add the exponents. For example, a^{m}* a^{n}= a^{m+n}.**Quotient of Powers:**When dividing powers with the same base, subtract the exponents. For example, a^{m}/ a^{n}= a^{m-n}.**Power of a Power:**When a power is raised to another power, multiply the exponents. For example, (a^{m})^{n}= a^{m*n}.**Zero Exponent:**Any non-zero number raised to the power of 0 is equal to 1. For example, a^{0}= 1.**Negative Exponent:**A negative exponent indicates the reciprocal of the base raised to the positive exponent. For example, a^{-n}= 1 / a^{n}.

Here are some key points to remember when studying powers:

- Understand the concept of a base and an exponent in a power expression.
- Practice calculating powers by multiplying the base by itself the number of times indicated by the exponent.
- Memorize the properties of powers and understand how to apply them in mathematical operations.
- Practice simplifying expressions involving powers using the properties of powers.

Remember to practice solving various problems involving powers to reinforce your understanding of the topic.

Good luck with your studies!

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.