i need help with this math problem?

Question

Use the properties of exponents to simplify this expression

(b^15)^8

 

i'm so confused 

Answer 1

What's happening here is that you have:

b¹⁵ * b¹⁵ * b¹⁵ * b¹⁵ * b¹⁵ * b¹⁵ * b¹⁵ * b¹⁵

When we multiply a similar base, we add the exponents together, like I said before, so this can be written as:
b^{15+15+15+15+15+15+15+15}

but can be short handed using multiplication as b^15*8

15 * 8 = 120

so the final answer is b¹²⁰

 

Remember the following rules:

a^b * a^c = a^{b + c}

 

(a^b)^c = a^{b * c}