Question

Simplify the two expressions:a.(-20632b.(-263)3Compare the solutions of both expressions. In the form of a paragraph, explain what affect an even exponent has on anegative number and what affect an odd exponent has on a negative number. Include the final answer in yourexplanation. Complete your work in the space provided or upload a file that can display math symbols if your workrequires it.

Answer 1

Simplify the expression;

`\begin{gathered} (a) \\ (-2a^4b^3)^2 \\ \end{gathered}`

We shall apply the rule of exponent which is;

`\begin{gathered} (-a)^n=a^n \\ \text{If n is an even number} \end{gathered}`

We now have;

`(-2a^4b^3)^2=(2a^4b^3)^2`

Next we shall apply the rule which is;

`(ab)^n=a^n* b^n=a^nb^n`

We now have the expression as;

`\begin{gathered} (2a^4b^3)^2 \\ =2^2*(a^4)^2*(b^3)^2^{} \\ =4* a^8* b^6 \\ =4a^8b^6 \end{gathered}`

For the (b) part;

`\begin{gathered} (b) \\ (-2a^4b^3)^3 \end{gathered}`

We shall apply the exponent rule;

`\begin{gathered} (-a)^n=-a^n \\ \text{If n is an odd number} \end{gathered}`

Our expression now becomes;

`\begin{gathered} (-2a^4b^3)^3 \\ =(-2a^4b^3)^3 \end{gathered}`

We shall also apply the second rule as stated earlier and we'll have;

`\begin{gathered} -2^3*(a^4)^3*(b^3)^3 \\ =-8* a^(12)* b^9 \\ =-8a^(12)b^9 \end{gathered}`

Step-by-step explanation:

An even exponent makes a negative number even as we have seen from our calculations. This is because the product of two negative numbers is positive, whereas an odd exponent makes a negative number odd because the product of three negative numbers like we saw in our calculation would be negative.

ANSWER:

`\begin{gathered} (a)4a^8b^6 \\ (b)-8a^(12)b^9 \end{gathered}`