Having a tought time with these
(x^4y^6z^12/9^-2x^3y^-8z^-9)^0
I am not sure why but i get the answer
1/9^0
I was thinking the ^0 multiplies everything to 0 but the 9.
(anything)^0 = 1 except 0^0 which is undefined.
I think all the ^ numbers are getting me confused.
So I am correct if I say the answer is 0. because everything there is multiplied by 0.
no, the answer is 1
an exponent of zero does not mean it is multiplied by zero, just like an exponent of 2 does not mean it is multiplied by 2
Ah ok, my answer = 1. This one really confused me.
To simplify the expression (x^4y^6z^12/9^-2x^3y^-8z^-9)^0, we need to understand the properties of exponents.
When an expression is raised to the power of 0, it always evaluates to 1. This is a fundamental property of exponents.
In this case, we have (x^4y^6z^12/9^-2x^3y^-8z^-9)^0.
To simplify this expression, we can rewrite the denominator 9^-2 as 1/9^2. Similarly, we can rewrite the negative exponents as 1 over the respective positive exponents. So, we have:
(x^4y^6z^12 / (1/9^2)x^3(1/y^8)(1/z^9))^0
Now, let's simplify the expression inside the parentheses:
(x^4y^6z^12 / (1/81)x^3(1/y^8)(1/z^9))^0
To divide fractions, we multiply by the reciprocal of the second fraction:
(x^4y^6z^12 / 1) * (81/x^3) * (y^8) * (z^9)
Now, with everything multiplied out, we can simplify further:
x^4 * y^6 * z^12 * 81/x^3 * y^8 * z^9
To multiply variables with the same base, we add their exponents:
x^(4-3) * y^(6+8) * z^(12+9) * 81
x^1 * y^14 * z^21 * 81
Now, we have (x * y^14 * z^21 * 81)^0. And as I mentioned earlier, any expression raised to the power of 0 equals 1.
Therefore, the simplified expression is 1.