Difference between revisions of "1959 AHSME Problems/Problem 5"
(Created page with "== Problem 5== The value of <math>\left(256\right)^{.16}\left(256\right)^{.09}</math> is: <math>\textbf{(A)}\ 4 \qquad \ \textbf{(B)}\ 16\qquad \ \textbf{(C)}\ 64\qquad \ ...") |
(No difference)
|
Revision as of 23:08, 5 July 2016
Problem 5
The value of is:
Solution
When we multiply numbers with exponents, we add tne exponents together and leave the bases unchanged. We can apply this concept to computate :
Now we can convert the decimal exponent to a fraction:
Now, let us convert the expression into radical form. Since
is the denominator of the fractional exponent, it will be the index exponent:
Since
, we can solve for the fourth root of
:
Therefore,