How do you express (3x^2)^-3 with positive exponents?

2 Answers
Shwetank Mauria
Sep 11, 2016

(3x^2)^(-3)=1/(27x^6)

Explanation:

We can use the identities a^(-m)=1/a^m, (a^m)^n=a^(mn) and (ab)^m=a^mb^m

Hence, (3x^2)^(-3)

= 1/(3x^2)^3

= 1/(3^3*(x^2)^3)

= 1/(27*x^(2xx3))

= 1/(27x^6

Tony B
Sep 18, 2016

1/(27x^6)

Explanation:

Method Example:

Suppose we had t^(-3). This is another way of writing 1/(t^3)

Suppose we had 1/(t^-3) this is another way of writing t^3

So the negative power (index) has the effect of moving the value to the other side of the horizontal line.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:" "(3x^2)^-3

The index -3 is acting on everything inside the brackets. So this is the same as:

1/(3x^2)^3" "->" "1/(3^3xx x^2 xx x^2 xx x^2)" "->" "1/(3^3x^(2xx3))

=1/(27x^6)

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