Laws Of Exponents

1. How to multiply powers with the same base?

If we have to multiply the powers which have the same base then we have to add the exponents.

a^{m} \times a^{n} = a^{m + n}

Example

8^{3} \times 8^{4} = 8^{3 + 4}= 8^{7}

2. How to divide powers with the same base?

If we have to divide the powers which have the same base then we have to subtract the exponents.

Example

3. How to take the power of a power?

If we have to take the power of a power then we have to multiply the exponents.

(am)n = amn

Example

(8^{3})^{4} = 8^{3 \times 4}= 8^{12}

4. How to multiply the powers with the same exponents?

If we have to multiply the powers where the base is different but exponents are same then we will multiply the base.

ambm = (ab)m

Example

8^{3}4^{3} = (8 \times 4)^{3}= 32^{3}

5. How to divide the powers with the same exponents?

If we have to divide the powers where the base is different but exponents are same then we will divide the base.

Example

6. Numbers with Exponent Zero

Any number with zero exponents is equal to one irrespective of the base.

7. Numbers with Exponent One

Any number with one as the exponent is equal to the number itself.

a1 = a

8. Power with a Negative Exponent

Negative exponents can be converted into positive exponents.

Example

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