prove, using the law of exponents, that the following is true
(2^4)^3=(64)^2
(use the same bases to rewrite the expression)
the second half of =(8)^2 (8)^2
=(4)^2 (2)^2 (4)^2 (2)^2
=(2)^2(2^2)(2^2)(2^2)(2^2)(2^2)
now the first part
(2^4)^3
2x2x2x2
2x2x2x2
2x2x2x2
so put both sides together and get
2x2x2x2=2x2x2x2
2x2x2x2=2x2x2x2
2x2x2x2=2x2x2x2
Is this correct?
Thanks for checking my work
( 2 ^ 4 ) ^ 3 = ( 2 ^ 3 ) ^ 4 = 8 ^ 4
64 ^ 2 = ( 8 ^ 2 ) ^ 2 = 8 ^ 4
but the question said it the expression should have the same base, so wouldn't you have to go further?
changing to the same base
(2^4^3
= 2^12
64^2
= (2^6)^2 = 2^12
therefore (2^4)^3 = 64^2
I thought having the same base meant having the same number if it can be in simplier form. that is why I made them all multiples of 2.
Thank you for your help
Yes, your work is correct!
To prove that (2^4)^3 = (64)^2 using the law of exponents, let's start by simplifying both sides of the equation.
On the left side, we have (2^4)^3. Using the power of a power rule, we can rewrite this as 2^(4*3) = 2^12.
On the right side, we have (64)^2. Since 64 is equal to 2^6, we can rewrite this as (2^6)^2 = 2^(6*2) = 2^12.
Now, we have 2^12 on both sides of the equation, which means they are equal.
Therefore, (2^4)^3 = (64)^2 is proven true using the law of exponents.