Simplify the expression;
[tex]\begin{gathered} (a) \\ (-2a^4b^3)^2 \\ \end{gathered}[/tex]We shall apply the rule of exponent which is;
[tex]\begin{gathered} (-a)^n=a^n \\ \text{If n is an even number} \end{gathered}[/tex]We now have;
[tex](-2a^4b^3)^2=(2a^4b^3)^2[/tex]Next we shall apply the rule which is;
[tex](ab)^n=a^n\times b^n=a^nb^n[/tex]We now have the expression as;
[tex]\begin{gathered} (2a^4b^3)^2 \\ =2^2\times(a^4)^2\times(b^3)^2^{} \\ =4\times a^8\times b^6 \\ =4a^8b^6 \end{gathered}[/tex]For the (b) part;
[tex]\begin{gathered} (b) \\ (-2a^4b^3)^3 \end{gathered}[/tex]We shall apply the exponent rule;
[tex]\begin{gathered} (-a)^n=-a^n \\ \text{If n is an odd number} \end{gathered}[/tex]Our expression now becomes;
[tex]\begin{gathered} (-2a^4b^3)^3 \\ =(-2a^4b^3)^3 \end{gathered}[/tex]We shall also apply the second rule as stated earlier and we'll have;
[tex]\begin{gathered} -2^3\times(a^4)^3\times(b^3)^3 \\ =-8\times a^{12}\times b^9 \\ =-8a^{12}b^9 \end{gathered}[/tex]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:
[tex]\begin{gathered} (a)4a^8b^6 \\ (b)-8a^{12}b^9 \end{gathered}[/tex]