Simplify ((3m^4t^5)^2)/(2t^7)

$\frac{{(3 m^{4} t^{5})}^{2}}{2 t^{7}}$

Step 1

Simplify the numerator.

Apply the product rule to $3 m^{4} t^{5}$ .

$\frac{{(3 m^{4})}^{2} {(t^{5})}^{2}}{2 t^{7}}$

Apply the product rule to $3 m^{4}$ .

$\frac{3^{2} {(m^{4})}^{2} {(t^{5})}^{2}}{2 t^{7}}$

Raise $3$ to the power of $2$ .

$\frac{9 {(m^{4})}^{2} {(t^{5})}^{2}}{2 t^{7}}$

Multiply the exponents in ${(m^{4})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 m^{4 \cdot 2} {(t^{5})}^{2}}{2 t^{7}}$

Multiply $4$ by $2$ .

$\frac{9 m^{8} {(t^{5})}^{2}}{2 t^{7}}$

Multiply the exponents in ${(t^{5})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 m^{8} t^{5 \cdot 2}}{2 t^{7}}$

Multiply $5$ by $2$ .

$\frac{9 m^{8} t^{10}}{2 t^{7}}$

Step 2

Cancel the common factor of $t^{10}$ and $t^{7}$ .

Factor $t^{7}$ out of $9 m^{8} t^{10}$ .

$\frac{t^{7} (9 m^{8} t^{3})}{2 t^{7}}$

Cancel the common factors.

Factor $t^{7}$ out of $2 t^{7}$ .

$\frac{t^{7} (9 m^{8} t^{3})}{t^{7} \cdot 2}$

Cancel the common factor.

$\frac{t^{7} (9 m^{8} t^{3})}{t^{7} \cdot 2}$

Rewrite the expression.

$\frac{9 m^{8} t^{3}}{2}$