[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
- Simplify ⇨ [tex]( 3 x ^ { 2 } ) ^ { - 3 }[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex]( 3 x ^ { 2 } ) ^ { - 3 }[/tex]
Use the rules of exponents to simplify the expression.
[tex]\left(3x^{2}\right)^{-3} [/tex]
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
[tex]3^{-3}\left(x^{2}\right)^{-3} [/tex]
Raise 3 to the power -3.
[tex] \longmapsto \: 3 ^{ - 3} \\ = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \\ = \frac{1}{27} [/tex]
Now, the whole equation becomes..
[tex]\frac{1}{27}\left(x^{2}\right)^{-3} \\ [/tex]
To raise a power to another power, multiply the exponents.
[tex]\frac{1}{27}x^{2\left(-3\right)} \\ [/tex]
Multiply 2 times -3.
[tex]\frac{1}{27}\times \left(\frac{1}{x^{6}}\right) \\ [/tex]
We can further simplify this to..
[tex] \frac{1}{27} \times \left(\frac{1}{x^{6}}\right) \\ = \frac{1}{27} \times \frac{1}{x ^{6} } \\ = \huge\boxed{ \boxed{\bf\frac{1}{27x^{6}}}}[/tex]
