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

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:

$\frac{x^5*y^6}{2^{-2}*x^0*x^9}$

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

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

$\frac{x^5*y^6}{2^{-2}*x^9}$

We can keep simplifying this.

We know that:

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

Then:

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

Then we get:

$\frac{x^5*y^6}{2^{-2}*x^9} = \frac{x^5*y^6}{x^9}*4$

And we also know that:

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

Then:

$\frac{x^5*y^6}{x^9}*4 = 4*y^6*\frac{x^5}{x^9} = 4*y^6*x^{5 - 9} = 4*y^6*x^{-4} = \frac{4*y^6}{x^4}$

And we can't simplify this anymore.