Question

Answer 1

a: \(a^3\cdot a^5=a^{3+5}=a^8\)

b: \(x^7\cdot x\cdot x^4=x^{7+1+4}=x^{12}\)

c: \(3^5\cdot4^5=\left(3\cdot4\right)^5=12^5\)

d: \(8^3\cdot2^3=\left(8\cdot2\right)^3=16^3\)

e: \(2^7\cdot5^7=\left(2\cdot5\right)^7=10^7\)

f: \(4^{10}\cdot8^{15}=\left(2^2\right)^{10}\cdot\left(2^3\right)^{15}=2^{20}\cdot2^{45}=2^{20+45}=2^{65}\)

g: \(4^{15}\cdot5^{30}=4^{15}\cdot\left(5^2\right)^{15}=\left(4\cdot5^2\right)^{15}=100^{15}\)

h: \(9^{12}\cdot3^5=\left(3^2\right)^{12}\cdot3^5=3^{24}\cdot3^5=3^{29}\)