# Simplify, `(3x^-4 d^5)^2 times 12cd^-4` give answer with non-negative exponents (3x to the -4 power d to the 5th power) squared times 12cd to the negative 4th power

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To simplify:

`(3x^-4 d^5)^2 times 12cd^-4`

First remove the breackets and use the rules of exponents by multiplying exponents due to the bracket:

`therefore = 3^2x^(-4 times2)d^(5 times2) times 12 c d^-4`

Now arrange in terms of the rules of exponents. Negartive exponents indicate division:

`therefore = (9 d^10)/x^8 times (12c)/d^4`

Now create one expression by combining like terms where appropriate:

`therefore = (108 c d ^(10-4))/x^8`

Note that the base "d" has been combined using the rules.

**Ans: **`therefore = (108cd^6)/x^8`