Answer:
We have the sentence:
"X by the power of 5 times y to the power of 6 over 2 by the power of -2 times x by the power of 0times x by the power of 9"
Let's break it into parts.
"X by the power of 5 times y to the power of 6..."
This can be written as:
x^5*y^6
"... 2 by the power of -2 times x by the power of 0times x by the power of 9"
This can be written as:
2^(-2)*x^(0)*x^(9)
And we have the quotient between the first thing and the second thing, then the equation is:
And any number by the power of 0 is equal to 1, then:
x^0 = 1, then we can rewrite the equation as:
We can keep simplifying this.
We know that:
a^(-n) = (1/a)^(n)
Then:
2^(-2) = (1/2)^2 = 1/4
Then we get:
And we also know that:
a^n/a^m = a^(n - m)
Then:
And we can't simplify this anymore.
Answer:
it's a perfect cube only....
Understanding the Question
This may not be the actual way that the US government prepares the CPI, but it will provide a comparison.
You can set up a proportion. The base number for the CPI is 38.8 in 1970. That number (38.8) has more than doubled to get to 82.4, which also tells us that there was inflation. What your parents and grandparents bought in 1970 went to double the amount in 1980. Gasoline certainly did that.
Givens
CPI in 1970 = 38.8
CPI in 1980 = 82.4
Eggs 1970 = 0.25
Edgs 1980 = X
Formula substitution and solution
CPI 1970 / CPI 1980 = cost of eggs 1970 / cost of eggs 1980
38.8/82.4 = 0.25 / x Cross multiply
38.8 * x = 0.25 * 82.4
38.8 * x = 20.625
x = 20.628 /38.8
x = 0.53 dollars of 53 cents.
53 cents in 1980 which is slightly double as predicted.
Footnote
As a matter of interest, my wife tells me that eggs now cost about 3.58 where we live. That's almost 7 times as expensive as they were in 1980. Something to think about. By the way, the price quoted is in Canada.
A right triangular prism is a solid that has faces that consist of 2 equilateral triangles and 3 congruent rectangles. It is also described to have two parallel faces and 3 other faces that belong to the same place (and are not parallel to the parallel pair of faces).
