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

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 = (×2²) × (× (1/2)³) × (×2⁴)

= 2² × (1/2)³ × 2⁴

= 2² × 2⁴ × (1/2)³

Using law of exponents,

a^m × aⁿ = a^{m + n}

= 2^{2 + 4} × (1/2)³

= 2⁶ × (1/2)³

= 2⁶/2³

Using law of exponents,

a^m ÷ aⁿ = a^{m - n}

= 2^{6 - 3}

= 2³

Therefore, (× 2³) 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

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

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

Summary:

A single repeater machine that will do the same work as the given hook-up is (× 2³).

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☛ Related Questions:

• Find a single repeater machine that will do the same work as each hook-up in figure (f)
• For each hook-up (figure a), determine whether there is a single repeater machine that will do the s . . . .
• For each hook-up (figure b), determine whether there is a single repeater machine that will do the s . . . .