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

Question

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

 Apr 17, 2023
 #1
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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,

 Apr 17, 2023
edited by BlackjackEd  Apr 17, 2023

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