Determine the value of the expression 4^3•4^-6

To solve this expression, we first perform the exponents:

4^3 = 4 x 4 x 4 = 64
4^-6 = 1 / 4^6 = 1 / 4096

Now, we multiply the two results together:

64 x 1 / 4096 = 0.015625

Therefore, the value of the expression 4^3 * 4^-6 is 0.015625.

what is that as a fraction?

To express the decimal value 0.015625 as a fraction, we can simply write it as a fraction with the decimal number as the numerator and powers of 10 as the denominator.

0.015625 = 15625 / 1000000

Both the numerator and denominator can be divided by 625 to simplify the fraction further:

15625 ÷ 625 = 25
1000000 ÷ 625 = 1600

Therefore, 0.015625 as a fraction is 25/1600.

can it be simplified in any way?

Yes, the fraction 25/1600 can be simplified further.

Both the numerator and denominator have a common factor of 25. Therefore, we can simplify by dividing both the numerator and denominator by 25:

25 ÷ 25 = 1
1600 ÷ 25 = 64

So, the simplified form of the fraction 25/1600 is 1/64.