Advertisements
Advertisements
Question
`(16 xx 10^2 xx 64)/(2^4 xx 4^2)`
Advertisements
Solution
Using laws of exponents,
am ÷ an = (a)m – n and am × an = am + n ...[∵ a is non-zero integer]
∴ `(16 xx 10^2 xx 64)/(2^4 xx 4^2) = (4)^2 xx 10^2 xx 2^-4 xx (4)^3 xx 4^-2` ...`[(∵ 64 = 4 xx 4 xx 4),(and 16 = 4 xx 4)]`
= (4)3 × 102 × 2–4
= (22)3 × 102 × 2–4
= 26 × 102 × 2–4
= 22 × 102 ...[∵ 22 = 4]
= 4 × 100
= 400
APPEARS IN
RELATED QUESTIONS
The reciprocal of `(2/5)^-1` is ______.
`(-5/7)^-5` is equal to ______.
The value of (7–1 – 8–1) –1 – (3–1 – 4–1) –1 is ______.
For any two non-zero rational numbers x and y, x4 ÷ y4 is equal to ______.
For a non-zero rational number p, p13 ÷ p8 is equal to ______.
Solve the following:
100–10
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.
- Make a table showing the insect’s location for the first 10 hops.
- Where will the insect be after n hops?
- Will the insect ever get to 1? Explain.
Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression 3–t. What fraction of substance remains after 7 half-lives?
For hook-up, determine whether there is a single repeater machine that will do the same work. If so, describe or draw it.
Find x.
`((-6)/7)^(x - 7) = 1`
