Question

Find the value of $(16{)}^{0.16}\times (16{)}^{0.04}\times (2{)}^{0.2}$.

• A. $1$
• B. $2$
• C. $4$
• D. $16$

Answer 1

The correct option is B $2$

We know that $x^a\times x^b=x^{a+b}$. We are going to use that principle here, and for that we need to have common base $x=2$. So, rewriting the given expression in scientific expression.

$(2^4{)}^{0.16}\times (2^4{)}^{0.04}\times 2^{0.2}$

Note that $(x^a{)}^b=x^{a\times b}$, that implies

$2^{4\times 0.16}\times 2^{4\times 0.04}\times 2^0.2=2^{4\times 0.16+4\times 0.04+0.2}=2^1=2$