Integers as Exponents – Explanation, Rules and Method of Solving

# Integers as Exponents – Explanation, Rules and Method of Solving

## What are Integer Exponents?

Integer exponents are a way of expressing a number in terms of its power. For example, the number 5 can be written as 5^1, which means that 5 is the first power (or exponent) of 5. The number 25 can be written as 5^2, which means that 5 is the second power of 5. And the number 125 can be written as 5^3, which means that 5 is the third power of 5.

Integer exponents can be used to simplify expressions. For example, the expression 5^2 + 5^3 can be simplified to 5^5.

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## 1. Product of Powers Rule

The product of powers rule states that if two or more powers are multiplied together, the result is the product of the individual powers. For example, if x is raised to the power y and z is raised to the power w, the result is xyz.

## 2. Quotient of Powers Rule

The quotient of powers rule states that the quotient of two powers is equal to the product of the two numbers that are being divided by each other, raised to the power of the difference of the two numbers.

## 3. Power of a Power Rule

The power of a power rule states that if a number is raised to a power, and that power is raised to a power, then the result is the number raised to the power of the product of the two powers.

For example, the power of a power rule states that if 5 is raised to the power of 3, then the result is 125.

## 4. Power of a Product Rule

The power of a product rule states that for any two real numbers a and b,

a(b+c) = ab+ac.

This rule can be used to simplify expressions that involve multiplication.

## 5. Power of a Quotient Rule

If a and b are real numbers and q is a rational number, then

(a/b)q = aq/bq.

## 6. Zero Power Rule

The zero power rule states that if a number is raised to the power of zero, the result is one.

## 7. Negativity Content Rule

a. No member shall post negative comments about other members or their work.

b. This rule does not apply to constructive criticism.

## How to Solve Integer Exponents?

There are a few ways to solve integer exponents. One way is to use the laws of exponents. Another way is to use the Order of Operations.

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