Find a single machine that will do the same job as the given hook-up
(c) a (× 5⁹⁹) machine followed by a (5^-100) machine.

Solution:

Given, two machines are hooked up.

a (× 5⁹⁹) machine followed by a (× 5^-100) machine.

We have to find a single machine.

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

Stretching power = (× 5⁹⁹) × (× 5^-100)

= 5⁹⁹ × 5^-100

Using law of exponents,

a^m × aⁿ = a^{m + n}

Here, a = 5

m = 99

n = -100

So, m + n = 99 + (-100)

= 99 - 100

= -1

So, 5⁹⁹ × 5^-100 = 5^-1

Therefore, (× 5^-1) does the same work as a (× 5⁹⁹) machine followed by (× 5^-100) machine.

✦ Try This: Find a single machine that will do the same job as the given hook-up

A (× 6⁹³) machine followed by a (6^-100) machine.

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

NCERT Exemplar Class 8 Maths Chapter 8 Problem 158(c)

Find a single machine that will do the same job as the given hook-up a (× 5⁹⁹) machine followed by a (5^-100) machine

Summary:

A single machine that will do the same job as a (× 5⁹⁹) machine followed by (× 5^-100) machine is (× 5^-1).

☛ Related Questions:

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