Brand X copier advertises that its copiers run 24% longer between service calls than its competitor. If Brand X copiers run 59,800 copies between services, how many copies would the competitor run?

The competitor will run 48,225.81 copies.

Step-by-step explanation:

Brand x copier run 59,800 copies between services

Brand X copiers run 24% longer between service calls than its competitor.

Let x = copies run by the competitor between services

Number of copies the competitor will run is

24% of x + x = 59,800

0.24x + x = 59,800

1.24x = 59,800

x= 59,800 / 1.24

x = 48,225.81

Therefore, the competitor will run 48,225.81 copies.

Wow. That's complicated.

I'll walk you through it though.

We're going to do this in three steps.

1. Simplify 7^1/3 * 7^5/3

When the base is the same, simply add/subtract the exponents.

7^1/3 * 7^5/3 = 7^6/3 = 7^2

Now we have the bottom simplified to 7^2, or 7^6/3

Now the overall equation is (7^2/3 / 7^6/3)^6

2.

When you're subtracting two numbers with exponents that have the same base, you simply subtract the exponents.

6 - 2 = 4

Now we're left with (7^4/3)^6

3.

When you have a base with an exponent, to the power of another exponent, you simply multiply the exponents.

4/3 * 6 = 24/3 = 8

The simplified form of the expression is 7^8. (This is your answer.)

Let me know if you have any other questions! :)