Algebra/Arithmetic/Exponent Problems



{ $$7^3=$${ 343_3 }
 * type="{}"}

{ $$5 + 4^2=$${ 21_3 }
 * type="{}"}

{ $$1,213 - 9^3=$${ 484_3 }
 * type="{}"}

{Calculating powers of 10 become easier when understanding that the exponent gives a clue to how many zeros there are after the 1.

For example, $$10^1 = 10$$, that is, 10 to the first power has one zero after the 1.

$$10^2 = 100$$, or $$10 \times 10 = 100$$ that is, 10 to the second power has two zeros after the 1.}

{ $$10^4=$${ 10,000|10000_14 }
 * type="{}"}

{ $$10^7=$${ 10,000,000|10000000_14 }
 * type="{}"}

{ $$10^{10}=$${ 10,000,000,000|10000000000_14 }
 * type="{}"}

{Everybody is born to $$2^1$$ biological parents. Our parents each had $$2^1 + 2^1$$ biological parents. We can say that our grandparents are $$2^2$$ mathematically as the number of our ancestors doubles with each generation we go back.

So:}

{How many times would 2 be multiplied to determine the number of great grandparents? { 3_3 }
 * type="{}"}

{How many times would 2 be multiplied to determine the number of great-great grandparents? { 4_3 }
 * type="{}"}

{How many people would be our 28 ancestors? { 256_3 }
 * type="{}"}

{We can identify the square numbers between two numbers by simply squaring basic numbers. For example:

To identify the square numbers between 20 and 40 we can say

$$4^2 = 16$$ is too small

$$5^2 = 25$$ is in the range

$$6^2 = 36$$ is in the range

$$7^2 = 49$$ is too large

So the square numbers in that range are 5 and 6.}

{Identify the square numbers between 50 and 100 inclusive. { 64_3 }, { 81_3 } and { 100_3 }
 * type="{}" coef="3"}

{Identify the square numbers between 160 and 200. { 169_3 } and { 196_3 }
 * type="{}" coef="2"}

{You tear a piece of paper in half. Then, you tear each remaining sheet of paper in half again. You tear the collection of papers 5 times over all. When you are done, how many scraps of paper do you have? { 32_2 }
 * type="{}"}