Question

Rewrite 81x^4y^8 as a power of a product

Answer 1

Answer:

34x4 • y8

Step-by-step explanation:

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Answer 2

81x^4y^8 as a power of a product= (3xy^4)^4.

To find,

A power of a product.

Given,

81x^4y^8

Solution,

To write 81x^4y^8 as a power of a product, we need to first factor the number 81 and variables x and y into their prime factors.

81 can be expressed as 3^4 and x^4 and y^8 are already in their prime factor form.

So,

81x^4y^8

can be written as

(3^4)(x^4)(y^8).

Now, we can write this expression as a power of a product.

(3xy^4)^4

This is because, (3xy^4) raised to the power of 4 is equal to (3^4)(x^4)(y^8).

When you have an expression in the form of x^m*y^n, where m and n are positive integers, it can be written as a power of a product in the following way:

x^my^n = (xy)^(m+n)

This means that you can take the product of x and y, raise it to the power of m+n, and this will be equivalent to the original expression.

For example, 81x^4y^8 can be written as:

81x^4y^8 = 3^4 * (x^2)^2 * (y^4)^2

= (3x^2y^4)^2

So, 81x^4y^8 can be written as a power of a product, which is (3x^2y^4)^2.

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