To simplify the expression [tex]\( (4 x^2 z^4)(5 x^2 z^3) \)[/tex], we need to follow these steps:
1. Multiply the coefficients:
- The first term in the expression [tex]\( 4 x^2 z^4 \)[/tex] has a coefficient of 4.
- The second term in the expression [tex]\( 5 x^2 z^3 \)[/tex] has a coefficient of 5.
- Multiply these coefficients together:
[tex]\[
4 \times 5 = 20
\][/tex]
2. Add the exponents of [tex]\( x \)[/tex]:
- In the expression [tex]\( 4 x^2 z^4 \)[/tex], the exponent of [tex]\( x \)[/tex] is 2.
- In the expression [tex]\( 5 x^2 z^3 \)[/tex], the exponent of [tex]\( x \)[/tex] is also 2.
- Add these exponents together:
[tex]\[
2 + 2 = 4
\][/tex]
3. Add the exponents of [tex]\( z \)[/tex]:
- In the expression [tex]\( 4 x^2 z^4 \)[/tex], the exponent of [tex]\( z \)[/tex] is 4.
- In the expression [tex]\( 5 x^2 z^3 \)[/tex], the exponent of [tex]\( z \)[/tex] is 3.
- Add these exponents together:
[tex]\[
4 + 3 = 7
\][/tex]
Putting it all together, the simplified form of the expression [tex]\( (4 x^2 z^4)(5 x^2 z^3) \)[/tex] is:
[tex]\[ 20 x^4 z^7 \][/tex]
Therefore, the correct answer is:
[tex]\[ 20 x^4 z^7 \][/tex]
