Question

simplify the following expression.
$(3y^{6})^{3} (-3y^{3}w^{9})^{3}$
show your work here
hint: to add an exponent ($x^{n}$), type \exponent\ or press \^\

Explanation:

Step1: Expand each term via power rule

First, apply the power of a product rule \((ab)^n = a^n b^n\) and power rule \((x^m)^n = x^{mn}\) to each factor:
For \((3y^6)^3\):
\(3^3 \cdot (y^6)^3 = 27y^{18}\)
For \((-3y^3w^9)^3\):
\((-3)^3 \cdot (y^3)^3 \cdot (w^9)^3 = -27y^9w^{27}\)

Step2: Multiply the two expanded terms

Multiply the coefficients and combine like variables using \(x^m \cdot x^n = x^{m+n}\):
\(27y^{18} \cdot (-27y^9w^{27}) = (27 \times -27) \cdot y^{18+9} \cdot w^{27}\)

Step3: Calculate final coefficients and exponents

Compute the coefficient sum and simplify variable exponents:
\(27 \times -27 = -729\), \(y^{18+9} = y^{27}\)
So the expression becomes \(-729y^{27}w^{27}\)

Answer:

\(-729y^{27}w^{27}\)