Find two repeater machines that will do the same work as a (× 81) machine.

Solution:

We have to find the two repeater machines that will do the same work as a (× 81) machine.

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

From the given figure,

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

Total work of the single machine = ×81

We know, 9² = 81

= 9² × 9²

We know, 9 = 3²

= 9² × (3²)²

Using the law of exponents,

(a^m)ⁿ = a^mn

= 9² × 3⁴

Now, machines with base 9, power 2 and base 3, power 4 can be hooked up to produce the same work.

Therefore, the required two repeater machines are (×9²) and (×3⁴).

✦ Try This: Find two repeater machines that will do the same work as a (× 64) machine.

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

NCERT Exemplar Class 8 Maths Chapter 8 Problem 165

Find two repeater machines that will do the same work as a (× 81) machine.

Summary:

(×9²) and (×3⁴) are two repeater machines that will do the same work as a (× 81) machine.

☛ Related Questions:

• Find a repeater machine that will do the same work as a (× 1/8) machine
• Find three machines that can be replaced with hook-ups of (× 5) machines
• The left column of the chart lists the lengths of input pieces of ribbon. Stretching machines are li . . . .