Properties of Exponents Calculator

'Properties of Exponents Calculator' is an online tool that helps to find the properties of exponents.

What are Properties of Exponents Calculator?

Online Properties of Exponents calculator helps you to find properties of exponents within a few seconds.

Properties of Exponents Calculator

NOTE: Enter the input values up to 3 digits only.

How to Use Properties of Exponents Calculator?

Please follow the below steps to find the properties of exponents:

• Step 1: Choose a drop-down list for given properties of exponents
• Step 2: Enter the base number, exponent number 1, and exponent number 2 in the given input box.
• Step 3: Click on the "Calculate" button to find the properties of exponents.
• Step 4: Click on the "Reset" button to clear the fields and find different exponent values.

How to Find Properties of Exponents? 

An exponent is defined as the number of times to multiply the base number by itself. In simple terms, how many times a particular number is multiplying to itself, is shown by using exponents.

There are different exponent rules:

• Product Property of Exponents

• Quotient Property of Exponents

• Zero Property of Exponents

• Negative Property of Exponents

Product property of exponents: The product property of exponents is used to multiply expressions with the same bases. This property says, "To multiply two expressions with the same base, add the exponents while keeping the base the same."

This rule involves adding exponents with the same base, a^m × aⁿ = a^{m + n}

Quotient Property of Exponents: The quotient property of exponents is used to divide expressions with the same bases. This property says, "To divide two expressions with the same base, subtract the exponents while keeping the base same."

This rule involves subtracting exponents with the same base, a^m / aⁿ = a^{m - n}

Zero Property of Exponents: The zero property of exponents is applied when the exponent of any base is 0. This property says, "Any number (other than 0) raised to 0 is 1." Note that 0⁰ is not defined

This rule involves irrespective of the base the value for a zero exponent is always equal to 1, a⁰ = 1

Negative Property of Exponents: The negative property of exponents is used when an exponent is a negative number. This property says, "To convert any negative exponent into positive exponent, the reciprocal should be taken

This rule involves the expression is transferred from the numerator to the denominator with the change in sign of the exponent values, a^-m = 1 / a^m

Solved Examples on Properties of Exponents Calculator

Example 1:

Divide 6⁴ and  6^1.

Solution:

=   6⁴ /  6¹  [As the base value are equal, divide powers with the same base, keep the base and subtract the exponents]

=  6^{4 -1} 

⁼  6³

Example 2:

Multiply 9³ and  9^10.

Solution:

=   9³ × 9¹⁰  [As the base value are equal, keep the base and add the exponents]

=  9^{3 + 10} 

⁼  9¹³

Example 3:

Divide 9⁵ and 3^4.

Solution:

=   9⁵ /  3⁴

=  (3²)⁵ / 3⁴

= 3¹⁰ / 3⁴ [As the base value are equal, divide powers with the same base, keep the base and subtract the exponents]

⁼  3^{10 - 4}

= 3⁶

Similarly, you can try the calculator to find the exponent values using exponents rules

1) Multiply 2¹⁰ and 2⁴

2) Divide 5¹⁰ and 5¹³

☛ Related Articles:

• Exponents
• Exponent Rules

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