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 GuideAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.