Answer:
Step-by-step explanation:
1). [tex]a^{3}\times a^5=a^8[/tex]
2). [tex](a^3)^3[/tex] = [tex]a^{9}[/tex]
3). [tex]\frac{a^{10}}{a^3}=a^{10-3}=a^7[/tex]
4). [tex]\frac{a^2}{a^7}=\frac{1}{a^{7-2}}=\frac{1}{a^5}[/tex]
5). [tex]\frac{a^5\times a^2}{a^7}=\frac{a^{5+2}}{a^7}=1[/tex]
6). [tex]\frac{16a^5b^3}{8a^2b}=(\frac{16\times 5}{8})(\frac{a^5}{a^2})(\frac{b^3}{b})[/tex]
[tex]=\frac{80}{8}(a^{5-2})(b^{3-1})[/tex]
= 10a³b²
7). [tex]\frac{2a^3b^3}{2b^2}=(\frac{2}{2})(a^3)(\frac{b^3}{b^2})[/tex]
= a³b
8). [tex](\frac{a^{-8}}{b^{11}})^{-2}=(\frac{b^{11}}{a^{-8}})^2[/tex]
[tex]=(b^{11}a^8)^2[/tex]
= [tex]a^{16}b^{22}[/tex]
9). [tex]\frac{(2a^3)(a^4)^2}{8a^{11}}=(\frac{2}{8})(\frac{1}{a^{11-3}})(a^4)^2[/tex]
[tex]=\frac{1}{4}(\frac{a^8}{a^8})[/tex]
[tex]=\frac{1}{4}[/tex]
10). [tex]\frac{5a^7b^2}{15a^{10}b^{-3}}=(\frac{5}{15})(\frac{a^7}{a^{10}})(b^{2+3})[/tex]
[tex]=\frac{1}{3}(\frac{b^5}{a^3} )[/tex]
[tex]=\frac{b^5}{3a^2}[/tex]
11). 3a⁰ = 3(1) = 3
12). (a²b)⁴ = (a²)⁴(b)⁴
= a⁸b⁴
