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:
[tex]\frac{x^5*y^6}{2^{-2}*x^0*x^9}[/tex]
And any number by the power of 0 is equal to 1, then:
x^0 = 1, then we can rewrite the equation as:
[tex]\frac{x^5*y^6}{2^{-2}*x^9}[/tex]
We can keep simplifying this.
We know that:
a^(-n) = (1/a)^(n)
Then:
2^(-2) = (1/2)^2 = 1/4
Then we get:
[tex]\frac{x^5*y^6}{2^{-2}*x^9} = \frac{x^5*y^6}{x^9}*4[/tex]
And we also know that:
a^n/a^m = a^(n - m)
Then:
[tex]\frac{x^5*y^6}{x^9}*4 = 4*y^6*\frac{x^5}{x^9} = 4*y^6*x^{5 - 9} = 4*y^6*x^{-4} = \frac{4*y^6}{x^4}[/tex]
And we can't simplify this anymore.
