Advertisements
Advertisements
Question
Find a single repeater machine that will do the same work as hook-up.
Advertisements
Solution
Using law of exponents,
(am × an = am + n) ...[∵ a is non-zero integer]
Repeater machine can do the work is equal to `2^2 xx (1/2)^3 xx 2^4`
= `2^6 xx 1/2^3` ...`[∵ a^m/a^n = a^(m - n)]`
= 23
So, (× 23) single machine can do the same work.
APPEARS IN
RELATED QUESTIONS
If x be any non-zero integer, then x–1 is equal to ______.
For a non-zero rational number p, p13 ÷ p8 is equal to ______.
On multiplying ______ by 2–5 we get 25.
`(-8/2)^0 = 0`
Find the value of x so that `(5/3)^-2 xx (5/3)^-14 = (5/3)^(8x)`
The cells of a bacteria double in every 30 minutes. A scientist begins with a single cell. How many cells will be there after 24 hours?
An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop. So, she will be at `1/2` after one hop, `3/4` after two hops, and so on.
Will the insect ever get to 1? Explain.
In a repeater machine with 0 as an exponent, the base machine is applied 0 times. What do you think the value of 60 is?
The left column of the chart lists the lengths of input chains of gold. Repeater machines are listed across the top. The other entries are the outputs you get when you send the input chain from that row through the repeater machine from that column. Copy and complete the chart.
| Input Length | Repeater Machine | ||
| × 23 | |||
| 40 | 125 | ||
| 2 | |||
| 162 | |||
Simplify:
`(1/5)^45 xx (1/5)^-60 - (1/5)^(+28) xx (1/5)^-43`
