Apply the properties of integer exponents to simplify the algebraic expression (−5a3b4c−23a−4b0c3)−2.(1 point)
Responses
−5c103a14b8
Start Fraction negative 5 c superscript 10 baseline over 3 a superscript 14 baseline b superscript 8 baseline End Fraction
c10a14b8
Start Fraction c superscript 10 baseline over a superscript 14 baseline b superscript 8 baseline End Fraction
9c1025a14b8
Start Fraction 9 c superscript 10 baseline over 25 a superscript 14 baseline b superscript 8 baseline End Fraction
925a12
Start fraction 9 over 25 a^12 b^8 c^10 end fraction
To simplify the expression (−5a^3b^4c^−2)^−2, you can apply the properties of integer exponents.
First, let's simplify the expression inside the parentheses: -5a^3b^4c^-2.
To simplify the negative exponent, we can rewrite it as its reciprocal: c^-2 = 1 / c^2.
Now our expression becomes -5a^3b^4 / c^2.
Next, we raise this expression to the power of -2. To do this, we invert the base and change the exponent's sign: (c^2 / (-5a^3b^4))^2.
Simplifying further, we square each term inside the parentheses: (c^2)^2 / ((-5a^3b^4)^2).
This gives us c^4 / (25a^6b^8).
Therefore, the simplified expression is c^4 / (25a^6b^8).