Question

A rocket ship is travelling at an average speed of 1.75 × 104 miles per hour. How many miles will the rocket ship travel in 1.2 × 102 hours?

1. Write the expression: (1.75 × 104)(1.2 × 102)

2. Rearrange the expression: (1.75 × 1.2)(104 × 102)

3. Multiply the coefficients: (2.1)(104 × 102)

4. Apply the product of powers: 2.1 × 10y

The rocket ship will travel 2.1 × 10y miles. What is the value of y in the solution?

y =

Answer 1

y = 6

Explanation:

Here you need to remember the relation:

Distance = Time*Speed.

In this case we know that:

Speed = 1.75*10^4 mi/hr

Time = 1.2*10^2 hours.

Then the distance equation is:

D = (1.75*10^4 mi/hr)*(1.2*10^2 hr)

Here we can rewrite the product as:

D = (1.75 mi/hr*1.2 hr)*(10^4*10^2)

D = (2.1 mi)*(10^4*10^2) = (2.1 mi)*(10^y)

We want to find the value of y.

Now we have a property for the product of powers:

Remember that:

`A^n*A^m = A^(n + m)`

Then:

D = (2.1mi)*(10^(4 + 2)) = (2.1mi)*(10^6)

D = 2.1*10^6 miles

This means that the value of y is 6.