Question

1. simplify

$(-2a^{4})(3ab^{2})(-5c^{0})$

Explanation:

Step1: Simplify the constant term $c^0$

Any non-zero number to the power of 0 is 1, so $c^0 = 1$. The expression becomes:
$(-2a^4)(3ab^2)(-5 \times 1) = (-2a^4)(3ab^2)(-5)$

Step2: Multiply the numerical coefficients

Multiply the constants together:
$(-2) \times 3 \times (-5) = 30$

Step3: Multiply the $a$-variable terms

Use exponent rule $a^m \times a^n = a^{m+n}$:
$a^4 \times a = a^{4+1} = a^5$

Step4: Combine all terms

The $b^2$ term has no like terms to combine, so we multiply it with the results from Step2 and Step3.

Answer:

$30a^5b^2$