Find a single repeater machine that will do the same work as each hook-up in figure (b).

Solution:

Given, the figure represents the work done by each hook-up.

We have to find a single repeater machine.

A repeater machine is a hypothetical machine which automatically enlarges items several times.

We know that, when two machines are hooked up their stretching power is multiplied.

Stretching power = (×100²) × (×100¹⁰)

= 100² × 100¹⁰

Using law of exponents,

a^m × aⁿ = a^{m + n}

Here, a = 100

m = 2

n = 10

So, m + n = 2 + 10

= 12

100² × 100¹⁰ = 100¹²

Therefore, (× 100¹²) does the same work as the given hook up.

✦ Try This: Find a single repeater machine that will do the same work as each hook-up.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 159(b)

Find a single repeater machine that will do the same work as each hook-up in figure (b).

Summary:

A single repeater machine that will do the same work as the given hook-up is (× 100¹²).

☛ Related Questions:

• Find a single repeater machine that will do the same work as each hook-up in figure (c)
• Find a single repeater machine that will do the same work as each hook-up in figure (d)
• Find a single repeater machine that will do the same work as each hook-up in figure (e)