Product of Powers

Product of Powers

How to solve the product of powers problems: examples and their solutions.

Example 1

Simplify the given expression. (2^3)*(2^2)

23 means multiplying 2 3 times.
(2 × 2 × 2)

And 22 means multiplying 2 2 times.
(2 × 2)

So 23 × 22 means multiplying 2, 3 + 2, 5 times.
(2 × 2 × 2 × 2 × 2)

This is 25.

How to read powers:

a2: a squared
a3: a cubed

an: a to the (power of) n(th),
 a raised to the nth power

Example 2

Simplify the given expression. (x^6)*(x^8)

'Multiplying x 6 times'
times 'multiplying x 8 times'
is multiplying x, 6 + 8, 14 times.

Example 3

Simplify the given expression. (3ab^4)*((3^2)(a^3)(b^7))

If the bases (the number below the power)
are the same,
then the exponents can be added.
(same colored exponents)