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

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 = (×7¹⁰) × (×7⁵⁰) × (× 7¹)

= 7¹⁰ × 7⁵⁰ × 7¹

Using law of exponents,

a^m × aⁿ = a^{m + n}

7¹⁰ × 7⁵⁰ = 7^{10 + 50}

= 7⁶⁰

Now, 7⁶⁰ × 7¹ = 7^{60 + 1}

= 7⁶¹

Therefore, (× 7⁶¹) does the same work as the given hook up.

✦ Try This: For each hook-up, determine whether there is a single repeater machine that will do the same work. If so, describe or draw it.

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

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

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

Summary:

A single repeater machine that will do the same work as the given hook-up is (× 7⁶¹).

☛ Related Questions:

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