Simplify each exponential expression:

Question

(- 5 x^{3} y^{2}) (- 2 x^{- 11} y^{- 2})

Accepted Answer

Hello everyone in this video we'll be simplifying the exponential expression, parentheses negative 12 A. To the fourth B to the seventh, parentheses parentheses again negative 482 negative seven beats the negative third. And in this case it can be kind of scary to approach this simplification because there's so many components and exponents and parentheses. However you can see that the parentheses help us group the different components And in each set of parentheses there's a number for the first set of parentheses. This number is -12. In the second set it's negative four followed by an a component age of the fourth or eight negative seven and a B component B to the seventh or B to the negative third. So you can see that once we identify the like terms in each set of parentheses we can sort of group. The multiplication is that we are going to follow. So the first set we have negative 12. And if we multiply it with the like term on the second set of parentheses, the like term is -4. So negative 12 times negative four is equal to positive 48. And if we follow the second set of like terms which is the a components we have a to the 4th Times 8 to -7. We know that when we multiply exponents together with the same base it becomes addition. So four plus negative seven not leaves A. To the negative three and then our last set of light terms is to be components where we have B to the 7th And that is being multiplied by B to the -3. And just like with our A. Term we're gonna add the exponents together. And that leaves us with B. To the fourth. So now if we combine All of the terms that we've just solved we have 48 times a. To the negative three And B to the 4th. Now recall that whenever you have a negative exponents, let's say A. To the negative B. You can rewrite this as a fraction Where it becomes one divided by A. To the B. And notice how the negative on the Be disappeared. So in this case we want to rewrite a -3 as a fraction and that becomes one divided by A. To the 3rd. So now This becomes Times B to the 4th times One divided by a 2/3. And if we combine all of these terms together it becomes 48 B. To the fourth divided by A. To the third. So this becomes our final answer and this is also our final answer or it could be our final answer. We've simply rewriting it in fraction form in the boxed solution here and you can see that our solution aligns with answer choice D. Hopefully this video helped and see you next time

Simplify each exponential expression: $(- 5 x^{3} y^{2}) (- 2 x^{- 11} y^{- 2})$

Key Concepts

Laws of Exponents

Multiplication of Algebraic Expressions

Handling Negative Exponents

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