What is 4 to the power of -3 written as a power of 2? Please explain how you work this out...?

Just remember this rule:


(a^b)^c = a^(bc)





Replace 4 with 2虏





4^(-3)


= (2虏)^(-3)


= 2^(-6)





Note: You could invert the exponent and put it in the denominator, but then you'd just have to invert it again and put it in the numerator. Save yourself a couple steps...





What is 4 to the power of -3 written as a power of 2? Please explain how you work this out...?
a^(-b)= 1/(a^b)...


first property to be used


now...


usin above property ... a is 4.....b is 3...


we get 1/(4^3)...


by law of exponents ... 4 can be written as 2^2...


and theres a rule...


a^b^c = a^(bc)...


therefore... now we finally get ... 1/(2^2^3)...


= 1/(2^6)


=2^(-6)


gotit?


last two steps are tow wayss of showin the answerWhat is 4 to the power of -3 written as a power of 2? Please explain how you work this out...?
4^-3 = 1/(4^3)





but we know that 4 = 2^2 so we sub in this





4^-3 = 1/ ((2^2)^3)


= 1/(2^6)


(finally bring the power to the top by changing its sign)





= 2^-6
Here's the easiest way:


4^1 = 4


4^2 = 4*4 = 16


4^3 = 4*4*4 = 64


so 4^-3 = 1/64





64 = 2*2*2*2*2*2 = 2^6


so 1/64 = 2^-6


.



4^(-3)=1/(4^3)


4=2^2


1/(4^3)=1/((2^2)^3)


=1/(2^6)


or


2^(-6)
4^(-3) = 1 / 4鲁 = 1 / 64 = 1 / 2^6
4^-3 = (2^2)^-3 = 2^-6 = 1/2^6 = 1/64



(4^-3)^2?





IF that is then it should be 1/32
Use that:


a^(-b)=1/a^b





(a^b)^c=a^(bc)






well 4 is the same as 2^2


so:


4^(-3) = 2^[2(-3)] = 2^(-6)