What is the simplified form of (1 point) Responses Image with alt text: Start Fraction 81 a superscript 4 baseline c superscript 3 baseline over b superscript 2 baseline End Fraction Image with alt text: Start Fraction 81 a superscript 4 baseline over b superscript 2 baseline c superscript 3 baseline End Fraction Image with alt text: Start Fraction 3 a superscript 4 baseline over b superscript 2 baseline c superscript 3 baseline End Fraction
The simplified form of 81a^4c^3/b^2 is 3a^4c^3/b^2.
To find the simplified form of the given expression, we need to simplify each term in the numerator and the denominator separately.
Let's start with the numerator: 81a^4c^3.
To simplify this term, we notice that 81 is a perfect cube. Hence, we can rewrite it as (3^4). Now, we have:
(3^4)a^4c^3.
Next, let's simplify the denominator: b^2c^3.
Now, we can express the entire fraction as:
(3^4)a^4c^3 / b^2c^3.
To simplify this fraction, we can divide the common factors between the numerator and denominator. In this case, we have c^3 as a common factor.
Dividing the common factor, we get:
(3^4)a^4 / b^2.
So, the simplified form of the expression is:
(3^4)a^4 / b^2.
To simplify the expression (81a^4c^3)/(b^2), follow these steps:
1. Rewrite the numerator and denominator with prime factorization:
(3^4 * 3^4 * a^4 * c^3) / (b^2)
2. Simplify the exponents by combining like bases:
(3^(4+4) * a^4 * c^3) / (b^2)
3. Add the exponents:
(3^8 * a^4 * c^3) / (b^2)
Therefore, the simplified form of the expression (81a^4c^3)/(b^2) is (3^8 * a^4 * c^3) / (b^2).