Simplify the expression: 12dn3/15cd3 / 9c3n/10c2d2

Question

ScanSolve AI Tutor · Accepted Answer

To simplify the expression, we will first convert the division into multiplication by taking the reciprocal of the second fraction.

Rewrite the division as multiplication.
$\frac{12dn^3}{15cd^3} \div \frac{9c^3n}{10c^2d^2} = \frac{12dn^3}{15cd^3} \times \frac{10c^2d^2}{9c^3n}$
Multiply the numerators and the denominators.
$\frac{12dn^3 \times 10c^2d^2}{15cd^3 \times 9c^3n}$
Group the numerical coefficients and the variables.
$\frac{(12 \times 10) \times (d \cdot d^2) \times (n^3) \times (c^2)}{(15 \times 9) \times (c \cdot c^3) \times (d^3) \times (n)}$ $\frac{120 d^{1+2} n^3 c^2}{135 c^{1+3} d^3 n}$ $\frac{120 d^3 n^3 c^2}{135 c^4 d^3 n}$
Simplify the numerical coefficients by dividing by their greatest common divisor, which is 15.
$\frac{120 \div 15}{135 \div 15} = \frac{8}{9}$
Simplify the variables using the exponent rule $\frac{x^a}{x^b} = x^{a-b}$ .
For $d$ : $\frac{d^3}{d^3} = d^{3-3} = d^0 = 1$
For $n$ : $\frac{n^3}{n} = n^{3-1} = n^2$
For $c$ : $\frac{c^2}{c^4} = c^{2-4} = c^{-2} = \frac{1}{c^2}$
Combine the simplified numerical and variable parts.
$\frac{8}{9} \times 1 \times n^2 \times \frac{1}{c^2} = \frac{8n^2}{9c^2}$
The simplified expression is:
$\frac{8n^2}{9c^2}$

Simplify the expression: (12dn3)/(15cd3) / (9c3n)/(10c2d2)