Multiply Algebraic Terms with Powers

This activity is about the multiplication of algebraic terms with powers.

Example

Simplify:

2a³b × 5a⁴b²

Answer

Break down what 2a³b and 5a⁴b² mean and multiply them.

We get:    

2 × a × a × a × b × 5 × a × a × a × a × b × b

Bring the numbers to the front and separate the letters to get:

2 × 5 × a × a × a × a × a × a × a × b × b × b

This gives us

10 × a × a × a × a × a × a × a × b × b × b

which simplifies to

10a⁷b³

Quick method

Simplify:

2a³b × 5a⁴b²

Answer

Take the terms one at a time.

Start by multiplying the numbers (2 × 5 = 10).

Then deal with the indices of identical letters by adding the powers:  for a: 3 + 4 = 7 and for b: 1 + 2 = 3

Answer is 10a⁷b³.

Shall we try some questions now?