Math Snap

STEP 1

What is this asking?
Multiply these two algebraic expressions together and simplify the result.
Watch out!
Remember your exponent rules, and don't forget that a means a¹!

STEP 2

1. Rewrite the expression
2. Multiply the coefficients
3. Multiply the variables

STEP 3

Alright, let's rewrite our problem to make it super clear what we're multiplying!
We have $(5ab)(ab^2)$.
Remember that a is the same as a¹ and b is the same as b¹.
So, let's rewrite it as $(5a^1b^1)(a^1b^2)$.
This makes it much easier to see what's going on!

STEP 4

Now, let's multiply those coefficients!
We have a 5 in the first term and an invisible 1 in front of the second term.
So, $5 \cdot 1 = \textbf{5}$.
Easy peasy!

STEP 5

Time to tackle those variables!
When we multiply variables with the same base, we add their exponents.
Let's start with a.
We have a¹ times a¹.
So, $1+1=2$, which gives us a².

STEP 6

Now for the b's.
We have b¹ times b².
Adding those exponents, we get $1+2=3$, which gives us b³.

STEP 7

Let's put it all together!
We have our coefficient 5, a², and b³.
So, our final expression is $5a^2b^3$!

$5a^2b^3$