Math Snap

STEP 1

What is this asking?
We need to simplify the expression $(-4x^4y^7)^2$.
Watch out!
Don't forget to square everything inside the parentheses, including the $-4$!
And remember your exponent rules!

STEP 2

1. Distribute the exponent.
2. Simplify the terms.

STEP 3

Alright, let's distribute that exponent of $2$ to each term inside the parentheses.
Remember, this means we're multiplying the exponents of each term by $2$.
Why? Because raising a power to a power means we multiply the exponents!
It's like saying we have two sets of parentheses multiplied together, each containing $-4x^4y^7$.

STEP 4

So, we have $(-4)^2 \cdot (x^4)^2 \cdot (y^7)^2$.
See how we applied the exponent to each piece?
This is super important!

STEP 5

Let's simplify each part.
First, $(-4)^2$ means $-4$ times $-4$, which gives us a positive 16.
Remember, a negative times a negative is a positive!

STEP 6

Next, $(x^4)^2$.
When we raise a power to a power, we multiply the exponents.
So, $4 \cdot 2 = 8$, giving us $x^8$.

STEP 7

Finally, $(y^7)^2$.
Again, multiply those exponents: $7 \cdot 2 = 14$, resulting in $y^{14}$.

STEP 8

Putting it all together, we have $16x^8y^{14}$.
Boom!

Our simplified expression is $16x^8y^{14}$.