Exponents (Indices) grade 6-7 worded problem

Question

I am a a student and I am having difficulty with answering this question. Please may I have a step by step solution to this question so that I won't have difficulties with answering these type of questions in the future.

A car travels at at a speed $7^2$ miles per hour, how long will the car travel in $7^7$ days?

I did this:

$24$ hours $\cdot 7^7 = 168^7$

$168^7 \cdot 7^2 = 1174^9$

The answer I got was $1174^9$. However, it is wrong.

Thank you and help would be appreciated.

Answer 1

Well you can't write $24 \cdot 7^7 = (24 \cdot 7)^7$. In fact you can't simplyfy the left side anymore. It would be better if you just multiply the time with the speed and you will get:

$$24\cdot 7^7 \cdot 7^2 = 24 \cdot 7^{7+2} = 24 \cdot 7^9$$

If you want you can calculate the value of $7^9$, which is a pretty large number.