Question

Simplify this expression: (a^2b^4c)^-2 x (ab^2c^2)

a) a^4b^6c^2
b) a^-2b^-2c^2
c) a^0b^2c^2
d) a^2b^6c^2

Answer 1

To simplify the expression (a^2b^4c)^-2 x (ab^2c^2), we can first move the negative exponent to the denominator and distribute the exponent to each term inside the parentheses. Then, we can multiply the fractions and combine like terms. The final simplified expression is a^(-3)b^6.

Step-by-step explanation:

To simplify the expression (a^2b^4c)^-2 x (ab^2c^2), we can use the properties of exponents.

1. First, when we raise a number to a negative exponent, we can move it to the denominator and make the exponent positive. So, (a^2b^4c)^-2 becomes 1/(a^2b^4c)^2.
2. Next, we can distribute the exponent of 2 to each term inside the parentheses, giving us 1/(a^4b^8c^2).
3. Finally, we multiply this result by the remaining terms, which is (ab^2c^2). So, the simplified expression is (1/(a^4b^8c^2)) x (ab^2c^2).
4. When we multiply the two fractions, we can combine like terms in the numerator and denominator. In this case, we have a^4 in the denominator and a in the numerator, b^8 in the denominator and b^2 in the numerator, and c^2 in the denominator and c^2 in the numerator. So, the final simplified expression is a^(-3)b^6c^0, which can be written as a^(-3)b^6.