Math  /  Algebra

Question(5a3b)(2a2b4)\left(5 a^{3} b\right)\left(-2 a^{2} b^{4}\right)

Studdy Solution

STEP 1

What is this asking? Multiply these two algebraic expressions together! Watch out! Don't forget the rules of exponents!
And watch those signs!

STEP 2

1. Rewrite the expression
2. Group like terms
3. Multiply the coefficients
4. Multiply the variables

STEP 3

Alright, let's **rewrite** this bad boy to make it super clear what we're dealing with!
We've got (5a3b)(2a2b4)(5a^3b)(-2a^2b^4).
Remember, parentheses next to each other mean **multiplication**!

STEP 4

Let's **group** our like terms together so we can see exactly what we're multiplying.
We've got coefficients (the numbers in front) and then we've got *a* terms and *b* terms.
So, we can rewrite our expression as (52)(a3a2)(bb4)(5 \cdot -2)(a^3 \cdot a^2)(b \cdot b^4).
See how much clearer that is?!

STEP 5

Time to **multiply** those coefficients!
We have 52=105 \cdot -2 = -10.
Remember a positive times a negative is a negative!

STEP 6

Now for the fun part – **multiplying** the variables!
Remember the rule: when multiplying like bases, we *add* the exponents.

STEP 7

For the *a* terms, we have a3a2=a3+2=a5a^3 \cdot a^2 = a^{3+2} = a^5.
We're adding those exponents, 3 plus 2, to get 5!

STEP 8

For the *b* terms, we have bb4=b1+4=b5b \cdot b^4 = b^{1+4} = b^5.
Remember, if you don't see an exponent, it's secretly a 1!
So, 1 plus 4 gives us 5.

STEP 9

Now, let's put it all together!
We have 10-10, a5a^5, and b5b^5.
So our **final expression** is 10a5b5-10a^5b^5!

STEP 10

10a5b5-10a^5b^5

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