Simplify (18st^4)/(52s^3t)*(16s^3)/(9s^2t)

$\frac{18 s t^{4}}{52 s^{3} t} \cdot \frac{16 s^{3}}{9 s^{2} t}$

Step 1

Combine.

$\frac{18 s t^{4} (16 s^{3})}{52 s^{3} t (9 s^{2} t)}$

Step 2

Multiply $s$ by $s^{3}$ by adding the exponents.

Move $s^{3}$ .

$\frac{18 (s^{3} s) t^{4} \cdot 16}{52 s^{3} t (9 s^{2} t)}$

Multiply $s^{3}$ by $s$ .

Raise $s$ to the power of $1$ .

$\frac{18 (s^{3} s^{1}) t^{4} \cdot 16}{52 s^{3} t (9 s^{2} t)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{18 s^{3 + 1} t^{4} \cdot 16}{52 s^{3} t (9 s^{2} t)}$

Add $3$ and $1$ .

$\frac{18 s^{4} t^{4} \cdot 16}{52 s^{3} t (9 s^{2} t)}$

Step 3

Multiply $s^{3}$ by $s^{2}$ by adding the exponents.

Move $s^{2}$ .

$\frac{18 s^{4} t^{4} \cdot 16}{52 (s^{2} s^{3}) t (9 t)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{18 s^{4} t^{4} \cdot 16}{52 s^{2 + 3} t (9 t)}$

Add $2$ and $3$ .

$\frac{18 s^{4} t^{4} \cdot 16}{52 s^{5} t (9 t)}$

Step 4

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$\frac{18 s^{4} t^{4} \cdot 16}{52 s^{5} (t \cdot t) \cdot 9}$

Multiply $t$ by $t$ .

$\frac{18 s^{4} t^{4} \cdot 16}{52 s^{5} t^{2} \cdot 9}$

Step 5

Cancel the common factor of $18$ and $52$ .

Factor $2$ out of $18 s^{4} t^{4} \cdot 16$ .

$\frac{2 (9 s^{4} t^{4} \cdot 16)}{52 s^{5} t^{2} \cdot 9}$

Cancel the common factors.

Factor $2$ out of $52 s^{5} t^{2} \cdot 9$ .

$\frac{2 (9 s^{4} t^{4} \cdot 16)}{2 (26 s^{5} t^{2} \cdot 9)}$

Cancel the common factor.

$\frac{2 (9 s^{4} t^{4} \cdot 16)}{2 (26 s^{5} t^{2} \cdot 9)}$

Rewrite the expression.

$\frac{9 s^{4} t^{4} \cdot 16}{26 s^{5} t^{2} \cdot 9}$

Step 6

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 s^{4} t^{4} \cdot 16}{26 s^{5} t^{2} \cdot 9}$

Rewrite the expression.

$\frac{s^{4} t^{4} \cdot 16}{26 s^{5} t^{2}}$

Step 7

Cancel the common factor of $s^{4}$ and $s^{5}$ .

Factor $s^{4}$ out of $s^{4} t^{4} \cdot 16$ .

$\frac{s^{4} (t^{4} \cdot 16)}{26 s^{5} t^{2}}$

Cancel the common factors.

Factor $s^{4}$ out of $26 s^{5} t^{2}$ .

$\frac{s^{4} (t^{4} \cdot 16)}{s^{4} (26 s t^{2})}$

Cancel the common factor.

$\frac{s^{4} (t^{4} \cdot 16)}{s^{4} (26 s t^{2})}$

Rewrite the expression.

$\frac{t^{4} \cdot 16}{26 s t^{2}}$

Step 8

Cancel the common factor of $t^{4}$ and $t^{2}$ .

Factor $t^{2}$ out of $t^{4} \cdot 16$ .

$\frac{t^{2} (t^{2} \cdot 16)}{26 s t^{2}}$

Cancel the common factors.

Factor $t^{2}$ out of $26 s t^{2}$ .

$\frac{t^{2} (t^{2} \cdot 16)}{t^{2} (26 s)}$

Cancel the common factor.

$\frac{t^{2} (t^{2} \cdot 16)}{t^{2} (26 s)}$

Rewrite the expression.

$\frac{t^{2} \cdot 16}{26 s}$

Step 9

Cancel the common factor of $16$ and $26$ .

Factor $2$ out of $t^{2} \cdot 16$ .

$\frac{2 (t^{2} \cdot 8)}{26 s}$

Cancel the common factors.

Factor $2$ out of $26 s$ .

$\frac{2 (t^{2} \cdot 8)}{2 (13 s)}$

Cancel the common factor.

$\frac{2 (t^{2} \cdot 8)}{2 (13 s)}$

Rewrite the expression.

$\frac{t^{2} \cdot 8}{13 s}$

Step 10

Move $8$ to the left of $t^{2}$ .

$\frac{8 t^{2}}{13 s}$

Simplify (18st^4)/(52s^3t)*(16s^3)/(9s^2t)

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