anonymous one year ago simplify 15 exponent 18 over 15 exponent 3

1. anonymous

post the multiple choice pls

2. anonymous

A)15 exponent 6 B)15 exponent 15 C)1 exponent 6 D)1 exponent 15

3. jtvatsim

The question is $\frac{15^{18}}{15^{3}}$ right?

4. anonymous

yes

5. anonymous

its asking me to simplify that

6. jtvatsim

OK, the important thing to remember about exponents is that they usually represent multiplying the same thing over and over. So for example, $15^3 = 15 \times 15 \times 15$. where the exponent 3 tells me to multiply 15 three times. Does that make sense as an example?

7. anonymous

yes, thank you but based on the multiply choice what is the answer

8. jtvatsim

Of course, that's the next step. :) I'll help you figure it out by asking you a couple questions. It's not too hard. :) Let's think about the top part of the fraction. How many times do I multiply 15 when I have an exponent of 18?

9. anonymous

18 times

10. jtvatsim

Excellent! So we know that our fraction looks like this...

11. anonymous

:T

12. jtvatsim

$\frac{15 \times 15 \times \cdots \times 15 \ (18 \text{\times}))}{15 \times 15 \times 15}$

13. jtvatsim

There are eighteen 15s on top, and three 15s on the bottom. There's going to be cancellations!

14. anonymous

i know

15. jtvatsim

Good, we get to cancel three 15s, which leaves us with fifteen 15s on top.

16. marihelenh

Dividing the two is also equal to$15^{18-3}$ It will get you the same answer.

17. jtvatsim

The final answer is that we have fifteen 15s multiplied together. This is the same as $15^{15}$ we are done!

18. anonymous

Thanks

19. jtvatsim