Laws of Exponents explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
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Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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An exponent shows repeated multiplication.
Exponent laws help us simplify long products and quotients written with powers.
They are used in algebra, large numbers, scientific notation, area, volume, and growth.
In , 2 is the base and 5 is the exponent. It means 2 x 2 x 2 x 2 x 2.
The base is the number being multiplied. The exponent tells how many times the base is used as a factor.
Exponent laws work when the base rules match. For example, x works because the base a is the same.
A power can be simplified by counting repeated factors carefully.
Meaning: The base is multiplied repeatedly. The exponent counts the factors.
Definition: In , a is the base and n is the exponent.
Meaning: When multiplying powers with the same base, add the exponents.
Definition: x .
x because there are factors of 2.
Meaning: When dividing powers with the same base, subtract the exponents.
Definition: , where a is not 0.
because two factors of 3 cancel.
Meaning: When a power is raised to another power, multiply the exponents.
Definition: .
means is repeated 3 times, so the exponent is 2 x .
Meaning: A noero number raised to 0 equals 1.
Definition: , where a is not 0.
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Easy
Question: Write 6 x 6 x 6 x 6 in exponent form.
Medium
Question: Simplify x .
Exam-level
Question: Simplify .
Multiplying exponents in the product law
Why it happens: Students mix up product law and power of a power.
Correct approach: For samase multiplication, add exponents.
Adding exponents in power of a power
Why it happens: The outside exponent is not understood.
Correct approach: For , multiply m and n.
Using exponent laws with different bases
Why it happens: Only the exponents are noticed.
Correct approach: Check the base first.
Treatin and as the same
Why it happens: Brackets are ignored.
Correct approach: Use brackets to show when the negative number is the base.
What is the difference between base and exponent?
The base is the number being multiplied. The exponent tells how many times it is used.
Can I add powers with the same base?
Exponent laws here apply to multiplication and division, not ordinary addition.
Why is equal to 1?
It follows from the quotient law when equal powers of a noero number are divided.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.