How to Multiply Exponents
Make sure the exponents have the same base., Add the exponents together., Calculate the expression.
Step-by-Step Guide
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Step 1: Make sure the exponents have the same base.
The base is the large number in the exponential expression.
You can only use this method if the expressions you are multiplying have the same base.
For example, you can use this method to multiply 52×53{\displaystyle 5^{2}\times 5^{3}}, because they both have the same base (5).
On the other hand, you cannot use this method to multiply 52×23{\displaystyle 5^{2}\times 2^{3}}, because they have different bases (5 and 2). -
Step 2: Add the exponents together.
Rewrite the expression, keeping the same base but putting the sum of the original exponents as the new exponent.For example, if you are multiplying 52×53{\displaystyle 5^{2}\times 5^{3}}, you would keep the base of 5, and add the exponents together:52×53{\displaystyle 5^{2}\times 5^{3}}=52+3{\displaystyle =5^{2+3}}=55{\displaystyle =5^{5}} , An exponent tells you how many times to multiply a number by itself.You can use a calculator to easily calculate an exponential expression, but you can also calculate by hand.
For example 55=5×5×5×5×5{\displaystyle 5^{5}=5\times 5\times 5\times 5\times 5}55=3,125{\displaystyle 5^{5}=3,125}So, 52×53=3,125{\displaystyle 5^{2}\times 5^{3}=3,125} -
Step 3: Calculate the expression.
Detailed Guide
The base is the large number in the exponential expression.
You can only use this method if the expressions you are multiplying have the same base.
For example, you can use this method to multiply 52×53{\displaystyle 5^{2}\times 5^{3}}, because they both have the same base (5).
On the other hand, you cannot use this method to multiply 52×23{\displaystyle 5^{2}\times 2^{3}}, because they have different bases (5 and 2).
Rewrite the expression, keeping the same base but putting the sum of the original exponents as the new exponent.For example, if you are multiplying 52×53{\displaystyle 5^{2}\times 5^{3}}, you would keep the base of 5, and add the exponents together:52×53{\displaystyle 5^{2}\times 5^{3}}=52+3{\displaystyle =5^{2+3}}=55{\displaystyle =5^{5}} , An exponent tells you how many times to multiply a number by itself.You can use a calculator to easily calculate an exponential expression, but you can also calculate by hand.
For example 55=5×5×5×5×5{\displaystyle 5^{5}=5\times 5\times 5\times 5\times 5}55=3,125{\displaystyle 5^{5}=3,125}So, 52×53=3,125{\displaystyle 5^{2}\times 5^{3}=3,125}
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Shirley Howard
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