Question

Express $ {16^{ - 2}}$ as a power of base 2.

Answer 1

Hint: One number can be represented with the base being any other number. In this case the number should be in some power of the base. Otherwise, the exponent obtained will be fraction and not the whole number. It is advised to know the exponents of smaller numbers up to 5.

Complete step-by-step solution:
The given question is $ {16^{ - 2}}$
We need to express this in terms of power with base 2.
The given number 16 can be represented as $ 2 \times 2 \times 2 \times 2$
$ \Rightarrow 16 = {2^4}$
In the question we are given
$ {16^{ - 2}}$
It can be re written as,
 $ {({2^4})^{ - 2}} \\
 \Rightarrow {(2)^{4 \times ( - 2)}} = {2^{ - 8}} $
So the number $ {16^{ - 2}} = {2^{ - 8}}$

Note: The change in the base may give change in the power but the ultimate value obtained will be the same. If someone gets confused he/she is advised to retrace from bottom to top in order to correct the solution.
We can apply this knowledge and reduce lengthy fractional problems into simpler ones.