Question

question 9
this is the only question in this section.
question
fully simplify using only positive exponents.
(5a⁸b⁰c⁻³)(-3a⁻⁴c⁻²)

Explanation:

Step1: Simplify $b^0$ rule

Any non-zero term to the 0 power is 1, so $b^0=1$. The expression becomes:
$(5a^8 \cdot 1 \cdot c^{-3})(-3a^{-4}c^{-2}) = (5a^8c^{-3})(-3a^{-4}c^{-2})$

Step2: Multiply constant coefficients

Multiply 5 and -3:
$5 \times (-3) = -15$

Step3: Combine $a$ terms (exponent addition)

Add exponents of like bases: $a^{8 + (-4)} = a^{4}$

Step4: Combine $c$ terms (exponent addition)

Add exponents of like bases: $c^{-3 + (-2)} = c^{-5}$

Step5: Convert negative exponent to positive

Use $x^{-n}=\frac{1}{x^n}$ for $c^{-5}$:
$c^{-5} = \frac{1}{c^5}$

Step6: Combine all simplified terms

Multiply the constant, $a$ term, and positive exponent $c$ term:
$-15 \cdot a^4 \cdot \frac{1}{c^5}$

Answer:

$\frac{-15a^4}{c^5}$