Answer:
[tex]-24\cdot x^{7}[/tex]
Step-by-step explanation:
We have been given an expression [tex](-2x^2)^3\cdot3x[/tex]. We are asked to find the product of our given expression.
Using exponent property [tex](a^b)^c=a^{b\cdot c}[/tex], we will get:
[tex](-2x^2)^3\cdot 3x=-2^3\cdot x^{2\cdot 3}\cdot3x[/tex]
[tex](-2x^2)^3\cdot 3x=-8\cdot x^{6}\cdot 3x[/tex]
[tex](-2x^2)^3\cdot 3x=-8\cdot 3\cdot x^{6}\cdot x[/tex]
[tex](-2x^2)^3\cdot 3x=-24\cdot x^{6}\cdot x[/tex]
Using exponent property [tex]a^b\cdot a^c=a^{b+c}[/tex], we will get:
[tex](-2x^2)^3\cdot 3x=-24\cdot x^{6+1}[/tex]
[tex](-2x^2)^3\cdot 3x=-24\cdot x^{7}[/tex]
Therefore, the product of our given expression would be [tex]-24\cdot x^{7}[/tex].
