What is 5xy^4z^5 * 8x^7z^2 ?

Answer 1

To multiply the expression \( 5xy^4z^5 \) by \( 8x^7z^2 \), you should multiply the coefficients and then multiply the variables, combining like terms.

1. Multiply the coefficients: \( 5 \times 8 = 40 \)

2. Multiply the variable \( x \): \( x^1 \times x^7 = x^{1+7} = x^8 \)

3. Multiply the variable \( y \): \( y^4 \) (since there is no \( y \) in the second expression, it remains \( y^4 \))

4. Multiply the variable \( z \): \( z^5 \times z^2 = z^{5+2} = z^7 \)

Now, combine all the results:

\[ 5xy^4z^5 \times 8x^7z^2 = 40x^8y^4z^7 \]

Thus, the final result is:

\[ \boxed{40x^8y^4z^7} \]