Question

a) 3^6.3^7=

b) x^10:x^6:x

c) a^5.a^9

d) 2^3.8^5.16^4

e) 25^3.5^5.3125

f) a^10.a^4:a^12

Answer 1

a) \(3^6.3^7\) \(=3^{13}\)

b) \(x^{10}:x^6:x\)

\(=x^{10}:x^7\)\(=x^3\)

c) \(a^5.a^9=a^{14}\)

Answer 2

\(a,=3^{6+7}=3^{13}\\ b,=x^{10-6-1}=x^3\\ c,=a^{5+9}=a^{14}\\ d,=2^3\cdot2^{15}\cdot2^{16}=2^{34}\\ e,=5^6\cdot5^5\cdot5^5=5^{16}\\ f,=a^{10+4-12}=a^2\)

Answer 3

d) \(2^3.8^5.16^4\)

\(=2^3.\left(2^3\right)^5.\left(2^4\right)^4\)

\(=2^3.2^{15}.2^{16}\)

\(=2^{34}\)

e) \(25^3.5^5.3125\)

\(=\left(5^2\right)^3.5^5.5^5\)

\(=5^6.5^5.5^5\)

\(=5^{16}\)

f) \(a^{10}.a^4:a^{12}\)

\(=a^{14}:a^{12}\)

\(=a^2\)