what is 1/4 to the power of 4 using exponents?

Question

Write −(1/4⋅1/4⋅1/4⋅1/4) using exponents.

huskylover2223 Apr 17, 2023

#1**+2 **

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,

BlackjackEd Apr 17, 2023