Question

simplify.
\\((-xy^{0}x^{4}a^{6})^{-3}\\)
\\((-xy^{0}x^{4}a^{6})^{-3}=\square\\) (use positive exponents only.)

Explanation:

Step1: Simplify $y^0$ rule

Any non-zero term to 0 power is 1: $y^0=1$
Expression: $(-x \cdot 1 \cdot x^4 a^6)^{-3} = (-x \cdot x^4 a^6)^{-3}$

Step2: Combine $x$ terms

Add exponents of like bases: $x^1 \cdot x^4 = x^{1+4}=x^5$
Expression: $(-x^5 a^6)^{-3}$

Step3: Apply negative exponent rule

Distribute $-3$ to each factor: $(ab)^n=a^n b^n$; $a^{-n}=\frac{1}{a^n}$
Expression: $\frac{1}{(-x^5 a^6)^3}$

Step4: Expand the denominator

Raise each factor to the 3rd power: $(-1)^3=-1$, $(x^5)^3=x^{15}$, $(a^6)^3=a^{18}$
Expression: $\frac{1}{-1 \cdot x^{15} a^{18}} = -\frac{1}{x^{15} a^{18}}$

Answer:

$-\frac{1}{x^{15}a^{18}}$