Get the answer to "How do you express (3x2)−3 with positive exponents?"

Caroline Lynn

Answered question

2022-02-03

How do you express

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

with positive exponents?

Johnathan Carpenter

Beginner2022-02-04Added 12 answers

Step 1
We can use the identities

a^{- m} = \frac{1}{a^{m}},

{(a^{m})}^{n} = a^{m n}

and

{(a b)}^{m} = a^{m} b^{m}

Hence,

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

= \frac{1}{{(3 x^{2})}^{3}}

= \frac{1}{27 \times x^{2 \times 3}}

= \frac{1}{27 x^{6}}

Ashly Forbes

Beginner2022-02-05Added 12 answers

Step 1
Method Example:
Suppose we had

t^{- 3}

. This is another way of writing

\frac{1}{t^{3}}

Suppose we had

\frac{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.
Step 2
Given:

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

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

\frac{1}{{(3 x^{2})}^{3}} \to \frac{1}{3^{3} \times x^{2} \times x^{2} \times x^{2}} \to \frac{1}{3^{3} x^{2 \times 3}}

= \frac{1}{27 x^{6}}

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