Simplify the expression. Write your answer using only positive exponents.
Explain as well.
1. (8x)^3*8^-4
2. 2x^-5*y^-3
3. (4x^4y^-3)^-2
4. 1/(3x)^-2
( 8 x ) ^ 3 * 8 ^ ( -4 ) =
8 ^ 3 * x ^ 3 / 8 ^ 4 =
8 ^ 3 * x ^ 3 / ( 8 ^ 3 * 8 ) =
[ ( 8 ^ 3 ) / ( 8 ^ 3 ) ] * ( x ^ 3 / 8 ) =
x ^ 3 / 8
2 x ^ ( - 5 ) * y ^ ( - 3 ) =
2 / ( x ^ 5 * y ^ 3 )
[ (4 x ^ 4 y ^ ( - 3) ] ^ ( - 2 ) =
[ ( 4 x ^ 4 / y ^ 3 ) ] ^ ( - 2 ) =
1 / ( 4 x ^ 4 / y ^ 3 ) ^ 2 =
1 / ( 16 x ^ 8 / y ^ 6 ) =
y ^ 6 / ( 16 x ^ 8 )
1 / ( 3 x )^ ( - 2 ) =
1 / [ 1 / ( 3 x ) ^ 2 ] =
1 / [ 1 / ( 9 x ^ 2 ) ] =
9 x ^ 2 / 1 =
9 x ^ 2