Question

Answer na following give the solution

Answer 1

The solution to the given indices are
`500 x^(14) y^(18)z^3` and
`3xy^3`

What is indices?

In mathematical expression, indices are expressions that consist of numbers and variables raised to their superscripts known as exponents. Solving indices helps to access the computational thinking and logic of the students.

From the given information;

`(2x)^2 (5xy^2)^3 (x^3y^4z)^3`

Using the appropriate rule, the first thing to do is to open the brackets.

`2^2 x^2 * 5^3 x^3y^6 * x^9y^(12)z^3`

Add exponents with common base:

`2^2 * 5^3 * x^(2+3+9) * y^(6+12) * z^3`

`500 * x^(14) * y^(18) * z^3`

`500 x^(14) y^(18)z^3`

`(27x^3y^4)/(9x^2y)`

Divide by using common factors.

`(3x^3y^4)/(x^2y)`

According to the rule of indices, subtract the exponents when dividing two similar terms together.

`3x^(3-2)y^(4-1)`

`3x^(1)y^(3)`

`3xy^3`