Simplify the expression using exponent rules. − 12 b 11 4 b 7 -\frac{12b^{11}}{4b^7} − 4 b 7 12 b 11

Hey, everyone. Welcome back. We have this practice problem here. Let's take a look. We have a negative 12 b to the 11th power divided by 4 b to the 7th power. Just as we've done with previous problems, we can always basically just separate the numbers with the numbers and the variables with the variables. So let's go ahead and do that. This really just becomes negative 12 divided by 4 times, and then we have b to the 11th divided by b to the 7th power. So how does this work out? Well, the number, just the, negative 12 over 4 just becomes negative 3. That's what this whole thing reduces to. And then what about this? Which rule of exponents am I gonna use here? I've got the same base, the b over here raised to 2 different powers, so this is gonna be the quotient rule. The quotient rule says that you're gonna divide or sorry, when you're dividing you're gonna subtract your exponents. So really this whole thing just becomes b to the 11 minuteus 7 power. So what does this simplify down to? Becomes negative b no, sorry, negative 3 b to the 4th power. And that is your final answer. I can't simplify this any further. So hopefully, that makes sense. Hopefully, you got it right, and thanks for watching.

Simplify the expression using exponent rules. − 12 b 11 4 b 7 -\frac{12b^{11}}{4b^7} − 4 b 7 12 b 11

− 3 b − 18 -3b^{-18} − 3 b − 18

− 3 b − 4 -3b^{-4} − 3 b − 4

0. Fundamental Concepts of Algebra

Exponents

Precalculus

0. Fundamental Concepts of Algebra

Exponents

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Multiple Choice

Simplify the expression using exponent rules.
$-\frac{12b^{11}}{4b^7}$

$-3b^{18}$

$-3b^{-18}$

$-3b^4$

$-3b^{-4}$

Verified step by step guidance

Start by simplifying the fraction $ \frac{-12b^{11}}{4b^7} $. Use the quotient rule for exponents, which states $ \frac{a^m}{a^n} = a^{m-n} $. Apply this rule to the expression.

Divide the coefficients: $ \frac{-12}{4} = -3 $. Then, apply the exponent rule to the variable part: $ b^{11-7} = b^4 $. This simplifies the fraction to $ -3b^4 $.

Next, consider the expression $ -3b^{18} $. This part does not need simplification as it is already in its simplest form.

Now, look at $ -3b^{-18} $. The negative exponent rule states $ a^{-n} = \frac{1}{a^n} $. Therefore, $ -3b^{-18} $ can be rewritten as $ -\frac{3}{b^{18}} $.

Combine the simplified expressions: $ -3b^4 $, $ -3b^{18} $, and $ -\frac{3}{b^{18}} $. The problem asks for the simplified form, which is $ -3b^4 $ or $ -3b^{-4} $ depending on the context of the problem.