Use the quotient rule to rewrite each expression, then simplify. − 12 b 11 4 b 7 -\frac{12b^{11}}{4b^7}

this problem, we're going to use the quotient rule to rewrite and simplify our expression, negative 12 times b to the eleventh power divided by four times b to the seventh power. So first, I'm going to break apart this quotient a little and think of this as instead negative 12 over four times b to the eleventh power over b to the seventh power. Now, we know that negative 12 divided by four is equal to negative three. And next, since our second quotient here, b to the eleventh over b to the seventh, has the same base value, we can apply our quotient rule by subtracting the exponents. So, we'll have b to the 11 minuteus seventh power, which all simplifies to negative three times b to the fourth power. And this is our expression 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.
$- \frac{12 b^{11}}{4 b^{7}}$

$-3b^4$

$-8b^4$

$b^4$

$-3b^{18}$

Verified step by step guidance

Identify the given expression as a quotient of two terms: $-\frac{12b^{11}}{4b^{7}}$.

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

Rewrite the expression by dividing the coefficients and subtracting the exponents of $b$: $-\frac{12}{4} \times b^{11-7}$.

Simplify the coefficient division: $-\frac{12}{4}$ becomes $-3$.

Combine the simplified coefficient and the power of $b$ to write the expression as $-3b^{4}$.

4:09m

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Struggling with Intermediate Algebra?

Use the quotient rule to rewrite each expression, then simplify.−12b114b7-\(\frac{12b^{11}\)}{4b^7}

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Use the quotient rule to rewrite each expression, then simplify.
$- \frac{12 b^{11}}{4 b^{7}}$