Question

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Answer 1

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• Simplify ⇨ $( 3 x ^ { 2 } ) ^ { - 3 }$

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$( 3 x ^ { 2 } ) ^ { - 3 }$

Use the rules of exponents to simplify the expression.

$\left(3x^{2}\right)^{-3}$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$3^{-3}\left(x^{2}\right)^{-3}$

Raise 3 to the power -3.

$\longmapsto \: 3 ^{ - 3} \\ = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \\ = \frac{1}{27}$

Now, the whole equation becomes..

$\frac{1}{27}\left(x^{2}\right)^{-3}$

To raise a power to another power, multiply the exponents.

$\frac{1}{27}x^{2\left(-3\right)}$

Multiply 2 times -3.

$\frac{1}{27}\times \left(\frac{1}{x^{6}}\right)$

We can further simplify this to..

$\frac{1}{27} \times \left(\frac{1}{x^{6}}\right) \\ = \frac{1}{27} \times \frac{1}{x ^{6} } \\ = \huge\boxed{ \boxed{\bf\frac{1}{27x^{6}}}}$