Question

Find the monomial if the expression is the cube of the monomial.
-0.001a to the power of 3n +3

Answer 1

To find the monomial whose cube is given by the expression \(-0.001a^{3n + 3}\), we can set up the equation as follows:

Let the monomial be \(x\).

Then we have:

\[
x^3 = -0.001a^{3n + 3}
\]

To find \(x\), we take the cube root of both sides:

\[
x = \sqrt[3]{-0.001} \cdot \sqrt[3]{a^{3n + 3}}
\]

Calculating the cube root of \(-0.001\):

\[
\sqrt[3]{-0.001} = -0.1
\]

Now, for the second part:

\[
\sqrt[3]{a^{3n + 3}} = a^{(3n + 3)/3} = a^{n + 1}
\]

Putting it all together, we find the monomial:

\[
x = -0.1 a^{n + 1}
\]

Thus, the monomial is:

\[
-0.1 a^{n + 1}
\]