+4 what is 1/4 to the power of 4 using exponents?
Question
Write −(1/4⋅1/4⋅1/4⋅1/4) using exponents.
+144
We already know that exponents mean you multiply the same number by itself. With fractions, the typical strategy is this:
When the
numerator = n,
denominator = d,
and the
exponent = x,
\( (n/d) ^x =(n ^x/d ^x)\)
Therefore, if we plug 1 in for n and 4 in for d with 4 as x, the equation becomes
\(1 ^4/4 ^4\)
We know that 1 to any power is itself, so we can simplify to
\(1/4 ^4\)
Now we can easily do 4 to the power of 4 in our heads, or you could plug it in a calculator if you'd like.
\(4*4*4*4=16*4*4=64*4=256\)
Knowing this, the equation becomes
\(1/256\)
To answer the full question (Write −(1/4⋅1/4⋅1/4⋅1/4) using exponents), all we have to do is put 1/256 inside the bracket, as we have evaluated what 1/4 to the power of 4 is, and simply place a negative sign next to it!
\(-1/256\)
Please correct me if I am wrong,
