Simplify (24a^2b^3c)/(16ab^-1c^2)

Problem

(24*a2*b3*c)/(16*a*b(−1)*c2)

Solution

1. Simplify the numerical coefficients by dividing both 24 and 16 by their greatest common divisor, which is 8.

24/16=3/2

2. Apply the quotient rule for exponents to the variable a by subtracting the exponent in the denominator from the exponent in the numerator.

(a2)/(a1)=a(2−1)=a1=a

3. Apply the quotient rule for exponents to the variable b remembering that subtracting a negative exponent is equivalent to addition.

(b3)/(b(−1))=b(3−(−1))=b(3+1)=b4

4. Apply the quotient rule for exponents to the variable c and move the result to the denominator to maintain a positive exponent.

(c1)/(c2)=c(1−2)=c(−1)=1/c

5. Combine the results into a single algebraic fraction.

(3⋅a⋅b4)/(2⋅c)

Final Answer

(24*a2*b3*c)/(16*a*b(−1)*c2)=(3*a*b4)/(2*c)

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