Question

1. $(-mp)(mp^{9})^{4}$ is equivalent to:

f. $m^{4}p^{36}$
g. $-m^{4}p^{36}$
h. $-m^{5}p^{37}$
j. $-m^{8}p^{40}$
k. $-m^{37}p^{37}$

Explanation:

Step1: Apply the power of a product rule

First, we deal with \((mp^{9})^{4}\). By the power of a product rule \((ab)^n=a^n b^n\), we have \((mp^{9})^{4}=m^{4}(p^{9})^{4}\).

Step2: Apply the power of a power rule

For \((p^{9})^{4}\), using the power of a power rule \((a^m)^n = a^{mn}\), we get \((p^{9})^{4}=p^{9\times4}=p^{36}\). So \((mp^{9})^{4}=m^{4}p^{36}\).

Step3: Multiply by \(-mp\)

Now we multiply \(-mp\) with \(m^{4}p^{36}\). Using the product rule for exponents \(a^m\times a^n=a^{m + n}\) for the same base:

• For the base \(m\): \(-m\times m^{4}=-m^{1 + 4}=-m^{5}\)
• For the base \(p\): \(p\times p^{36}=p^{1+36}=p^{37}\)

Combining these, we get \(-m^{5}p^{37}\).

Answer:

H. \(-m^{5}p^{37}\)