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. Functions

Exponent Rules

Business Calculus

0. Functions

Exponent Rules

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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

Step 1: Start by simplifying the fraction $-\frac{12b^{11}}{4b^7}$. Use the quotient rule for exponents, which states $\frac{a^m}{a^n} = a^{m-n}$, to simplify the powers of $b$. Divide the coefficients $-12$ and $4$ to get $-3$, and subtract the exponents $11 - 7$ to get $b^4$. The result is $-3b^4$.

Step 2: Combine the simplified term $-3b^4$ with the other terms in the expression: $-3b^{18}$ and $-3b^{-18}$.

Step 3: Notice that the terms $-3b^{18}$ and $-3b^{-18}$ are separate and do not combine with $-3b^4$ because they have different exponents. Each term remains distinct unless further operations are specified.

Step 4: If the problem asks for the correct answer to match $-3b^4$ or $-3b^{-4}$, verify that the simplified term $-3b^4$ aligns with the given solution. The other terms $-3b^{18}$ and $-3b^{-18}$ are not part of the final simplified expression.

Step 5: Conclude that the simplified expression is $-3b^4$, as it matches the correct answer provided in the problem.