Question

Write as a monomial in standard form.
(-X to the power of 2 ,y to the power of 3, m) to the power of 5

Answer 1

To write \((-x^2 y^3 m)^5\) as a monomial in standard form, we can use the rule of exponents \((a^m)^n = a^{m \cdot n}\) for each component inside the parentheses:

\[
(-x^2 y^3 m)^5 = (-1)^5 (x^2)^5 (y^3)^5 (m)^5
\]

Calculating each component:

1. \((-1)^5 = -1\)
2. \((x^2)^5 = x^{2 \cdot 5} = x^{10}\)
3. \((y^3)^5 = y^{3 \cdot 5} = y^{15}\)
4. \(m^5 = m^5\)

Putting it all together, we have:

\[
(-x^2 y^3 m)^5 = -1 \cdot x^{10} \cdot y^{15} \cdot m^5
\]

Thus, the final expression in standard form as a monomial is:

\[
-\ x^{10} y^{15} m^5
\]