Exponentiation is a mathematical operation that represents repeated multiplication of the same number. The number being multiplied is called the base, and the number of times it is multiplied by itself is called the exponent. The general format for exponentiation is:

base^{exponent}

For example, 2^{3} represents 2 multiplied by itself 3 times, which equals 8 (2 x 2 x 2).

**Product of Powers**: When multiplying two powers with the same base, add the exponents.- a
^{m}* a^{n}= a^{m+n} - Example: 2
^{3}* 2^{4}= 2^{7}

- a
**Quotient of Powers**: When dividing two powers with the same base, subtract the exponents.- a
^{m}/ a^{n}= a^{m-n} - Example: 3
^{5}/ 3^{2}= 3^{3}

- a
**Power of a Power**: When raising a power to another exponent, multiply the exponents.- (a
^{m})^{n}= a^{m * n} - Example: (4
^{3})^{2}= 4^{6}

- (a
**Power of a Product**: When raising a product to an exponent, distribute the exponent to each factor.- (ab)
^{n}= a^{n}* b^{n} - Example: (5 * 6)
^{2}= 5^{2}* 6^{2}

- (ab)

- Calculate 2
^{4}. - Simplify: 3
^{2}* 3^{5}. - What is the result of (7
^{3})^{2}? - Simplify: (4 * 9)
^{2}.

By mastering these properties and practicing the problems, you'll have a solid understanding of exponentiation. Good luck!

.Study GuideArea and Circumference of Circles Activity LessonArea of Circles Activity LessonCircumference of Circles Worksheet/Answer key

Area and Circumference of Circles Worksheet/Answer key

Area and Circumference of Circles Worksheet/Answer key

Area and Circumference of Circles Worksheet/Answer key

Area and Circumference of Circles

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

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

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.