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Laws of Exponents - Multiplying Powers with Different Base and Same Exponents

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Topics

formula

For any non-zero integer a, where m is any whole number, am × bm = (ab)m.

notes

Multiplying Powers with Different Base and Same Exponents:

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

In general, for any non-zero integer a, am × bm = (ab)m where m is any whole number.

(i) 23 × 33

= (2 × 2 × 2) × (3 × 3 × 3)

= (2 × 3) × (2 × 3) × (2 × 3)

= 6 × 6 × 6

= 63.....(Observe 6 is the product of bases 2 and 3)[am × bm = (a × b)m]

(ii) a4 × b4

= (ab)4 .................................[am × bm = (a × b)m]

Example

Express the following terms in the exponential form: (2 × 3)5.

(2 × 3)5

= (2 × 3) × (2 × 3) × (2 × 3) × (2 × 3) × (2 × 3)

= (2 × 2 × 2 × 2 × 2) × (3 × 3× 3 × 3 × 3)

= 25 × 35.

Example

Express the following term in the exponential form: (2a)4

(2a)4
= 2a × 2a × 2a × 2a

= (2 × 2 × 2 × 2) × (a × a × a × a)

= 24 × a4.

Example

Express the following term in the exponential form: (– 4m)3

(– 4m)3

= (– 4 × m)3

= (– 4 × m) × (– 4 × m) × (– 4 × m)

= (– 4) × (– 4) × (– 4) × (m × m × m)

= (– 4)3 × (m)3

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