I'm going to assume the equation you wrote is this:
(a^{5}•b^{0})^{3}
 = ?
(2b•a^{3})
The "cube" on the numerator's parentheses means
a5•b0 • a5•b0 • a5•b0
Since multiplying numbers means adding the exponents of the like terms, then
a^{(5+5+5)}•b^{(0+0+0)} = a^{15}•b^{0}
Thus you have
a^{15}•b^{0}
 = ?
2b•a^{3}
The zero exponent means "1", therefore
a^{15}•1
 = ?
2b•a^{3}
Multiplication is commutative, so you can rearrange the denominator
a^{15}•1
 = ?
a^{3}•2b
And you can combine like terms into separate fractions, like this
a^{15} 1
 •  = ?
a^{3} 2b
Dividing numbers means subtracting the exponents of the denominator from the exponents of the numerator, so
a^{(153)} = a^{12}
and
a^{12} 1
 •  = ?
1 2b
Recombining results in
a^{12}
 = ?
2b
So the answer is
(a^{5}•b^{0})^{3 } a^{12}
 = 
(2b•a^{3}) 2b
Of course, this is all assuming my interpretation of your problem is correct. Even if it's not, the principles shown here still hold.
Hope this helps!
10/8/2013

Nathan C.