# Math

How many integers are NOT perfect powers between 1 and 1000?

It might be easier to count how many are powers and subtract that number from 1000. To do this you should first find the highest power of 2 less than 1000, then you'll know how high of powers you have to count. You can check that
29 < 1000 < 210
so you'll need to check up to 9th powers.
For squares find the last square less than 1000 (this is 31^2)
then the last cube less than 1000
Skip fourth powers because they're also squares.
then the last fifth powers less than 1000
Skip sixth powers because they're also squares.
.
.
.
then the last ninth powers less than 1000

Be sure that you don't double count, because fourth, sixth eigth and tenth powers are also squares, so you really only need to look at prime powers.
You want the first square, cube, fifth, seventh and ninth powers such that they don't exceed 1000, but the next integer does, like 31 and 32 above.

1. 👍
2. 👎
3. 👁
1. Nine is not prime, so you skip it because the number will be in the cubes too

1. 👍
2. 👎

## Similar Questions

1. ### American government

What are powers of the U.S. government that are named and listed in the Constitution called? A.expressed powers B.implied powers C.inherent powers D.prohibited powers

2. ### civics

Which of the following are powers that are exercised by both the national government and state governments at the same time? A.concurrent powers B. enumerated powers C. prohibited powers D. reserved powers

3. ### American Government

the power of congress to print money is one of the legislative? A.Implied powers B.Expressed powers C.Inherent powers D.Nonlegislative powers

4. ### civics

The phrase, “the Elastic Clause,” comes from which powers of Congress? A.enumerated powers***** B.implied powers C.inherent powers D.reserved powers Please help asap

1. ### discrete math

Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. (b) have distinct digits. (c) are not

2. ### Civivs

The phrase, "the Elastic Clause," comes from which power of Congress?? A.) Enumerated Powers B.) Implied Powers C.) Inherent Powers D.) Reserved Powers This is Unit 2, Lesson 14: Unit Test: Three Branches of Government

3. ### check my work

1. Which of the following provides the best definition of a strict constructionist interpretation of congressional power? (1 point) Congress must have more powers than the states. Congress should only use implied powers when

4. ### MaTh

Find the sum of all positive integers less than 1000 ending in 3 or 7.

1. ### Civics

How do the powers of the national government and the powers of the states compare, according to James Madison, the primary author of the Constitution? A.The powers of the national government are few, while the powers of the states

2. ### Government

Homework Help Powers that are shared by both the National Government and the States are called... A) reserved powers B) enumerated powers C) inherent powers D) implied powers E) concurrent powers The Supreme Court carries out most

3. ### history

Which correctly describes the positive impact of European imperialism? Imperialist powers promoted their own interests over the well-being of indigenous peoples. Imperialist powers sought social change through self-government.

4. ### ALGEBRA.

The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?