Question

Xby the power of 5 times y to the power of 6 over 2 by the power of -2 times xby the power of 0times x by the power of 9

Answer 1

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:

`(x^5*y^6)/(2^(-2)*x^0*x^9)`

And any number by the power of 0 is equal to 1, then:

x^0 = 1, then we can rewrite the equation as:

`(x^5*y^6)/(2^(-2)*x^9)`

We can keep simplifying this.

We know that:

a^(-n) = (1/a)^(n)

Then:

2^(-2) = (1/2)^2 = 1/4

Then we get:

`(x^5*y^6)/(2^(-2)*x^9) = (x^5*y^6)/(x^9)*4`

And we also know that:

a^n/a^m = a^(n - m)

Then:

`(x^5*y^6)/(x^9)*4 = 4*y^6*(x^5)/(x^9) = 4*y^6*x^(5 - 9) = 4*y^6*x^(-4) = (4*y^6)/(x^4)`

And we can't simplify this anymore.