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When multiplying numbers in exponent notation with the**same base**, we can add the exponents.
^{2} × a^{3} = (a × a) × (a × a × a)

= a^{2 + 3}

= a^{5}

This is the**first law of exponents**:

a^{m} × a^{n} = a^{m + n}

^{3} × 3^{2}

b) x^{5} × x^{3}

^{3} × 3^{2} = 3^{3 + 2}

= 3^{5}

b) x^{5} × x^{3} = x^{5 + 3}

= x^{8}

^{m} + a^{n} ≠ a^{m + n}

Scroll down the page for more examples and solutions of the first law of exponents and also the other laws of exponents.

**Index rules - add and subtract indices**

Basic look at the first two index laws

**Properties of Exponents**

The Product Rule: a^{m} × a^{n} = a^{m + n}

The Quotient Rule: a^{m} ÷ a^{n} = a^{m - n}

The Power Rule: (a^{m})^{n} = a^{mn}

Example:

Simplify

(3ab^{4})(2a^{2}b)^{3}

(x^{2}y^{4}/2xz)^{3}

**Example of adding exponents**

(2a^{4})(5^{11})

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Arithmetic

Math Worksheets

When multiplying numbers in exponent notation with the

Consider:

a= a

= a

This is the

a

*Example:*

Simplify the following; give your answers in exponent form

a) 3b) x

* Solution: *

= 3

b) x

= x

** Common Error** : The first law of exponents does **NOT** apply to addition of numbers in exponent notation.

Scroll down the page for more examples and solutions of the first law of exponents and also the other laws of exponents.

Basic look at the first two index laws

The Product Rule: a

The Quotient Rule: a

The Power Rule: (a

Example:

Simplify

(3ab

(x

(2a

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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