Raising a Product or a Quotient to a Power.
(xy4)9
= x^9 y^36
To raise a product or a quotient to a power, you need to apply the power to each term or factor individually.
In the given expression (xy^4)^9, we have a product of two terms: xy^4. To raise this product to the power of 9, we will apply the power to each term separately.
First, let's focus on the first term, x. To raise x to the power of 9, we simply multiply x by itself 9 times:
x^9 = x * x * x * x * x * x * x * x * x
Now, let's look at the second term, y^4. To raise y^4 to the power of 9, we also multiply y^4 by itself 9 times:
(y^4)^9 = (y^4) * (y^4) * (y^4) * (y^4) * (y^4) * (y^4) * (y^4) * (y^4) * (y^4)
When multiplying powers with the same base, you add the exponents, so in this case, we add the exponents of y, which is 4:
(y^4)^9 = y^(4 * 9) = y^36
Finally, we combine the results for x and y^36:
(xy^4)^9 = x^9 * (y^4)^9 = x^9 * y^36
So, the expression (xy^4)^9 simplifies to x^9 * y^36.