Answer: a)
b) 27 c) 5 d)
![2^(12)=4096](https://img.qammunity.org/2021/formulas/mathematics/college/6arjat6luvrej73fbmzdsgkw0ionh6ggrj.png)
Explanation:
Properties of exponent :
![a^m* a^n= a^(m+n)](https://img.qammunity.org/2021/formulas/mathematics/college/amth2i24ek5lqx2mn4h0g5cuwkas822zz5.png)
![(a^m)/(a^n)=a^(m-n)](https://img.qammunity.org/2021/formulas/mathematics/college/mxcs5cw0k5bw9j352q2bzzrm4zzfyd1t7v.png)
![(a^m)^n=a^(mn)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/aut3rltwp06z5gg5a8b12dxcz7599tji5v.png)
![a^(-n)=(1)/(a^n)](https://img.qammunity.org/2021/formulas/mathematics/college/8l0zcej6cwaigvnukc6ttram4w95sfmj8l.png)
By using above properties we simplify the given expressions.
a)
![(5^3)/(25^2)=(5^3)/((5^2)^2)](https://img.qammunity.org/2021/formulas/mathematics/college/cz0gaau21d8ub4oqd3wsoeqtj012hnpmsj.png)
[ By using (3)]
[ By using (2)]
[ By using (4)]
b)
![(9^{(2)/(3)})(3)(3^{(3)/(2)})](https://img.qammunity.org/2021/formulas/mathematics/college/exy8ru9y4bcz3mq1nabrgtdctnvcsqvg4t.png)
[ By using (1)]
[ By using (3)]
[ By using (1)]
c)
![[(25)^(1)/(2)(5^2)]^{(1)/(3)} =[(5^2)^(1)/(2)(5^2)]^(1)/(3)](https://img.qammunity.org/2021/formulas/mathematics/college/lspp83h0ux6kp5376aek3hg5qj8tzpj4wa.png)
[ By using (3)]
[ By using (1)]
[ By using (3)]
d)
[ By using (5)]
[ By using (3)]
![=2^(6+6)=2^(12)=4096](https://img.qammunity.org/2021/formulas/mathematics/college/21ossjyt81zq203bycadm4nttgk7bpkp5r.png)