The rule for multiplying with exponents
1) In order to multiply you must have the same base!
ex: 3^2 * 3^5
3 is the base.
When you multiply exponents, just add the exponents together and keep the same base.
3^2 * 3^5 = 3^7
Visually, this is what it looks like.
3^2 = 3 * 3
3^5 = 3*3*3*3*3
Since we're multiplying them together...
3*3 *( 3*3*3*3*3)
All we do is count up how many times we're multiplying 3 by itself.
I count 7 times. That means 3 is being raised to the 7th power, or 3^7.
When you have an exponent raised to another exponent:
example (5²)³ [five squared, then cubed], if you work it out long way:
(5 * 5)³ = (5 * 5) * (5 * 5) * (5 * 5) = 56, so you multiply the exponents (2 * 6). This is just like multiplying being the same as repetitive addition.
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"Please Excuse My Dear Aunt Sally" Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. You do things in Parentheses first, followed by exponents, then multiplication and so on.
Brackets Exponents Division Multiplication Addition Subtraction
The Order of Operations is PEMDAS, which stands for Parentheses,Exponents, Multiplication,Division,Addition,Subtraction. OR Bedmas: Brackets Exponents Division Multiplication Addition Subtraction :) Or BIDMAS, where Exponent is replaced by Index
In the United States, the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS is often expanded to the mnemonic "Please Excuse My Dear Aunt Sally". This explains the order of operations. With no brackets, exponents are resolved first, then multiplication and division from left to right, then addition and subtraction from left to right.
BEDMAS Brackets Exponents Division Multiplication Subtraction Solve Brackets (parentheses) question first. (Ie 3(4)E2 =12E2) Then do the remaining exponents. (12E2 = 144) Division and Multiplication. Either can go first. (whichever order it appears in the question) Same with Addition and subtraction. Hope this helps!