Question

1. Write the expression:

Answer 1

Complete question is;

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 × 10^(y)

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

Answer:

Distance travelled by rocket ship = 2.1 × 10^(6) miles

y = 6

Step-by-step explanation:

1. The written expression;

(1.75 × 10⁴)(1.2 × 10²)

2. The rearranged expression is;

(1.75 × 1.2)(10⁴ × 10²)

3. Let's multiply the coefficient which is the first bracket to get;

2.1(10⁴ × 10²)

4. Applying the product of powers means we will add the powers of ten which are 4 and 2.

Thus; 2.1(10^(4 + 2)) = 2.1 × 10^(6) miles

Comparing to 2.1 × 10^(y), we have;

y = 6