Question

Question 20
The value of $(256{)}^{0.16}\times (256{)}^{0.09}$ is

A) 4
B) 16
C) 64
D) 256.25

Answer 1

The answer is A.
$(256{)}^{0.16}\times (256{)}^{0.09}=(256{)}^{\frac{16}{100}}\times (256{)}^{\frac{9}{100}}\left(256{)}^{\frac{16}{100}+\frac{9}{100}}\right[\because x^a.x^b=x^{a+b}]=({256}^{\frac{25}{100}})=(256{)}^{\frac{1}{4}}=(4^4{)}^{\frac{1}{4}}=4[\because (a^m{)}^n=a^{mn}]$