Use the quotient rule to rewrite each expression, then simplify. 9 x 2 y 8 3 x y 2 \frac{9x^2y^8}{3xy^2}

Here, we're going to use the quotient rule to rewrite and simplify our expression nine times x squared times y to the eighth divided by three times x times y to the second. So first, I'm going to break apart this quotient, So that way, I have my constants in one quotient times my x variables in another quotient times my y variables in my last quotient. And now I can simplify each of these individual quotients. We know that nine divided by three is three. Using our quotient rule, we know that x squared divided by x is x, and y to the eighth divided by y to the second is y to the eight minuteus two power, so y to the sixth power. And this is our expression now in its simplest form.

6. Exponents, Polynomials, and Polynomial Functions

The Quotient Rule

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

The Quotient Rule

Struggling with Intermediate Algebra?

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Multiple Choice

Use the quotient rule to rewrite each expression, then simplify.
$\frac{9 x^{2} y^{8}}{3 x y^{2}}$

$6 x y to the sixth power$

$3 x y to the sixth power$

$3x^2y^8$

$3x^2y^6$

Verified step by step guidance

Start with the given expression: $\frac{9x^2y^8}{3xy^2}$.

Apply the quotient rule for coefficients by dividing the numerical coefficients: $\frac{9}{3}$.

Apply the quotient rule for variables with exponents by subtracting the exponents of like bases in the denominator from those in the numerator: for $x$, compute $x^{2-1}$; for $y$, compute $y^{8-2}$.

Rewrite the expression using the simplified coefficients and variables: combine the results from the previous steps into a single expression.

Check the expression for any further simplification, such as reducing coefficients or combining like terms.

4:09m

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Struggling with Intermediate Algebra?

Use the quotient rule to rewrite each expression, then simplify.9x2y83xy2\frac{9x^2y^8}{3xy^2}

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Use the quotient rule to rewrite each expression, then simplify.
$\frac{9 x^{2} y^{8}}{3 x y^{2}}$