Simplify:
9^5 x^-3 y^15 z^-8
——————————
3^7 x^-4 y^11 z^5
move the variables to the numerator,change the 9 to 32
32*5 x-3+4y15-11 z-8-5/37
then move the 3 to the numerator.
32*5-7 x-3+4y15-11 z-8-5
Now combine exponents:
33 x1y4 z-13
Enough?
Yes tysm! :)
To simplify the given expression, we need to use the properties of exponents. Specifically, we can use the rules for multiplication and division of exponents.
Let's break down the expression step by step:
Step 1: Simplify the numerical coefficients:
9^5 / 3^7 = (3^2)^5 / 3^7 = 3^(2*5) / 3^7 = 3^10 / 3^7 = 3^(10-7) = 3^3 = 27
Step 2: Simplify the x-terms:
x^-3 / x^-4 = x^(-3-(-4)) = x^(-3+4) = x^1 = x
Step 3: Simplify the y-terms:
y^15 / y^11 = y^(15-11) = y^4
Step 4: Simplify the z-terms:
z^-8 / z^5 = z^(-8-5) = z^(-13) = 1/z^13
Combining all the simplified terms, we have:
27xy^4 / z^13
Therefore, the simplified expression is 27xy^4 / z^13.