Product of Powers

Multiplying Powers:

This is a power: 4⁵

4 is the base and 5 is the exponent.

This is 4 x 4 x 4 x 4 x 4

The base is the number being multiplied by itself.

The exponent tells how many times the base is being multiplied by itself.

Multiplying Powers:

What if I need to multiply powers?

For example: 3² x 3⁴

That would be: 3 x 3 x 3 x 3 x 3 x 3, which would be 3⁶

Multiplying Powers:

Let's try another:

For example: 5² x 5²

That would be: 5 x 5 x 5 x 5 , which would be 5⁴

Notice the bases are the same.

Multiplying Powers:

So, what seems to be happening?

When multiplying powers with the same base, we keep the base and add the powers.

Example: 3² x 3³ = 3 x 3 x 3 x 3 x 3 = 3⁵

​3 is a multiple 5 times.

Multiple Choice

Find the product. Write your answer using exponents.

$$2^2\ \times\ 2^3$$

• $$2^6$$

• $$2^5$$

• $$4^5$$

• $$4^6$$

Multiple Choice

Find the product. Write your answer using exponents.

$$5^2\ \times\ 5^4$$

• $$5^6$$

• $$10^6$$

• $$25^6$$

• $$5^8$$

Multiple Choice

Find the product. Write your answer using exponents.

$$x^2\ \times\ x^5$$

• $$2x^7$$

• $$x^7$$

• $$x^{10}$$

• $$2x^{10}$$

​What do you do if there are numbers and letters? Write.It.Out.

​2. 4ab(5a²b³) = 4 * a* b * 5 * a * a * b* b*b= 20a³b⁴

​1. b² * c⁴ * b³ = b*b *c*c*c*c* b*b*b = b⁵c⁴

Multiple Choice

Find the product. Write your answer using exponents.

$$a^2\ \times\ \ a^2$$

• $$2a^4$$

• $$a^4$$

• $$2a^2$$

Multiple Choice

Find the product. Write your answer using exponents.

$$3a^3\ \times\ \ a^2$$

• $$3a^5$$

• $$3a$$

• $$4a^5$$

Multiple Choice

Find the product. Write your answer using exponents.

$$d^4\ \times\ 4d^3$$

• $$5d^7$$

• $$4d^{12}$$

• $$4d^7$$

Multiple Choice

Simplify.

$$a^2b^3\left(a^2b^3\right)$$

• $$a^4b^6$$

• $$2a^22b^{6^{ }}$$

• $$2a^22b^3$$

• $$a^5b^5$$

Multiple Choice

Simplify.

$$2m^3\left(n^5m\right)$$

• $$2m^8n$$

• $$2m^4n^5$$

• $$2m^5n^4$$

• $$2m35n4$$

Multiple Choice

Find the missing exponent.

$$h^2\ \times\ h^?\ =\ h^7$$

• $$3$$

• 2

• 5

• 9