Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3y^−4/ 12x^7y^4

Answer 1

To generate an equivalent algebraic expression using the properties of integer exponents, we can use the following rules:

1. When dividing two terms with the same base, subtract the exponents:
\(x^m / x^n = x^{m-n}\)

2. When raising a power to another power, multiply the exponents:
\((x^m)^n = x^{mn}\)

3. When multiplying two terms with the same base, add the exponents:
\(x^m * x^n = x^{m+n}\)

Using these rules, we can simplify the given expression:
\(\frac{3x^3y^{-4}}{12x^7y^4}\)

First, simplify the coefficients: \(\frac{3}{12} = \frac{1}{4}\)

Next, simplify the variables:
\(x^3 / x^7 = x^{3-7} = x^{-4}\)

Finally, \(y^{-4} * y^4 = y^{(-4+4)} = y^0\)

Since \(y^0\) equals 1 (for any nonzero value of y), the expression becomes:
\(\frac{1}{4} * x^{-4} * 1\)

Simplifying further, we can write the equivalent algebraic expression as:
\(\frac{1}{4x^4}\)

Answer 2

Thats not an option

Answer 3

Apologies for the confusion. Let's correct the mistake.

The given expression is:

\(\frac{3x^3y^{-4}}{12x^7y^4}\)

To simplify this expression further, we can use the properties of exponents.

We start by simplifying the coefficients: \(\frac{3}{12} = \frac{1}{4}\)

Now let's simplify the variables:

For the x terms, we subtract the exponents: \(x^3 / x^7 = x^{3-7} = x^{-4}\)

For the y terms, we subtract the exponents: \(y^{-4} / y^4 = y^{-4-4} = y^{-8}\)

Putting it all together, the equivalent algebraic expression is:

\(\frac{1}{4x^4y^8}\)

So, \(\frac{3x^3y^{-4}}{12x^7y^4}\) is equivalent to \(\frac{1}{4x^4y^8}\).