Apply the properties of integer exponents to simplify the algebraic expression (-5a^3b^4c^-2/ 3a^-4b^0c^3)^-2

Answer 1

To simplify the given algebraic expression, (-5a^3b^4c^-2/3a^-4b^0c^3)^-2, we can apply the properties of integer exponents:

1) A negative exponent indicates the reciprocal of the base raised to the positive exponent.
2) Any base raised to the power of 0 equals 1.

Let's simplify the expression step by step:

(-5a^3b^4c^-2/3a^-4b^0c^3)^-2

First, deal with the negative exponents:

(-5a^3b^4c^-2/3 * 1/(a^-4) * 1/(b^0) * (c^3))^-2

Next, simplify the expressions with negative exponents by taking their reciprocal:

(-5a^3b^4/c^2 * a^4/3 * 1/(c^3))^-2

Now simplify the remaining exponents by multiplying:

(-5a^7b^4/3c^5)^-2

To get rid of the negative sign, we can take the reciprocal of the entire expression:

[1/(-5a^7b^4/3c^5)]^2

Simplify the expression inside the reciprocal:

[3c^5/(-5a^7b^4)]^2

Now, square each term within the brackets:

(3^2 * c^(5*2))/((-5)^2 * a^(7*2) * b^(4*2))

Simplify inside the brackets:

(9c^10)/(25a^14b^8)

Therefore, the simplified form of the given expression is (9c^10)/(25a^14b^8).