Use the quotient rule to rewrite each expression, then simplify. 30 x 5 y 3 z 3 − 15 x 2 y 3 z \frac{30x^5y^3z^3}{-15x^2y^3z}

this problem, we want to use the quotient rule to rewrite and simplify this expression. 30 times x to the fifth power times y to the third power times z to the third power, all divided by negative 15 times x squared times y to the third power times z. So my first step is I'm going to break apart each of these according to their common bases. So first, we'll break apart our constants as 30 over negative 15, and that will be multiplied by x to the fifth over x squared times y to the third over y to the third times z to the third over z. Now, I can simplify each of these quotients. So first, we know that 30 divided by negative 15 is negative two, x to the fifth divided by x to the second, we can use our quotient rule and subtract our exponents since we have a common base and we'll get x to the third power. Next, y cubed over y cubed will become y to the zeroth power, which is just one. And lastly, z to the third power divided by z is the same as z to the third power divided by z to the first power. So subtracting our exponents, we get z to the second power. And since anything multiplied by one is just the same thing, we can simplify this a little bit more and write this as negative two times x cubed times z squared. And this is our expression now in its simplest form.

Use the quotient rule to rewrite each expression, then simplify. 30 x 5 y 3 z 3 − 15 x 2 y 3 z \frac{30x^5y^3z^3}{-15x^2y^3z}

− 2 x 3 y 3 z 2 -2x^3y^3z^2 − 2 x 3 y 3 z 2

− 2 x 2 z 3 -2x^2z^3 − 2 x 2 z 3

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.
$\frac{30 x^{5} y^{3} z^{3}}{- 15 x^{2} y^{3} z}$

$2 x cubed z squared$

$negative 2 x cubed z squared$

$-2x^3y^3z^2$

$-2x^2z^3$

Verified step by step guidance

Identify the given expression as a quotient of two terms: $\frac{30x^5y^3z^3}{-15x^2y^3z}$.

Apply the quotient rule for exponents, which states that when dividing like bases, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.

Divide the coefficients (numerical parts) separately: divide 30 by -15 to simplify the numerical coefficient.

Subtract the exponents of each variable in the numerator by the corresponding exponents in the denominator: for $x$, $y$, and $z$, calculate $x^{5-2}$, $y^{3-3}$, and $z^{3-1}$ respectively.

Combine the simplified coefficient and variables with their new exponents to write the simplified expression.

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Use the quotient rule to rewrite each expression, then simplify.30x5y3z3−15x2y3z\frac{30x^5y^3z^3}{-15x^2y^3z}

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Use the quotient rule to rewrite each expression, then simplify.
$\frac{30 x^{5} y^{3} z^{3}}{- 15 x^{2} y^{3} z}$