Question 63030
{{{ (9ab^-2)^-2/(8a^-2b)^-2*(3a^-2b)^3/(2a^2b^-2)^3 }}}
Keep in mind that all numbers (without a shown exponent) have an understood exponent of 1
{{{ (9^1a^1b^-2)^-2/(8^1a^-2b^1)^-2*(3^1a^-2b^1)^3/(2^1a^2b^-2)^3 }}}
power to power rule: {{{ (x^m)^n = x^(mn) }}}
{{{ (9^-2a^-2b^4)/(8^-2a^4b^-2)*(3^3a^-6b^3)/(2^3a^6b^-6) }}}
If it has a negative exponent ... move to the other side of the fraction and make the exponent positive.
{{{ (b^4)(3^3b^3)(8^2b^6b^2)   /   (a^4)(2^3a^6)(9^2a^2a^6) }}}
Combine like terms by adding the exponents of the like variables
{{{ (b^15)(3^3)(8^2)   /   (a^18)(2^3)(9^2) }}}
Work the numbers
{{{ (27)(64)(b^15) / (8)(81)(a^18)  }}}
You can multiply and then reduce ... I prefer to reduce first
{{{ (1)(8)(b^15) / (1)(3)(a^18)  }}}
Multiply
{{{ 8b^15 / (3a^18) }}}