Simplify ((3rs^2t^4)^2)/(21r^2s^3t^11)

$\frac{{(3 r s^{2} t^{4})}^{2}}{21 r^{2} s^{3} t^{11}}$

Step 1

Simplify the numerator.

Apply the product rule to $3 r s^{2} t^{4}$ .

$\frac{{(3 r s^{2})}^{2} {(t^{4})}^{2}}{21 r^{2} s^{3} t^{11}}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $3 r s^{2}$ .

$\frac{{(3 r)}^{2} {(s^{2})}^{2} {(t^{4})}^{2}}{21 r^{2} s^{3} t^{11}}$

Apply the product rule to $3 r$ .

$\frac{3^{2} r^{2} {(s^{2})}^{2} {(t^{4})}^{2}}{21 r^{2} s^{3} t^{11}}$

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

$\frac{9 r^{2} {(s^{2})}^{2} {(t^{4})}^{2}}{21 r^{2} s^{3} t^{11}}$

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

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

$\frac{9 r^{2} s^{2 \cdot 2} {(t^{4})}^{2}}{21 r^{2} s^{3} t^{11}}$

Multiply $2$ by $2$ .

$\frac{9 r^{2} s^{4} {(t^{4})}^{2}}{21 r^{2} s^{3} t^{11}}$

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

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

$\frac{9 r^{2} s^{4} t^{4 \cdot 2}}{21 r^{2} s^{3} t^{11}}$

Multiply $4$ by $2$ .

$\frac{9 r^{2} s^{4} t^{8}}{21 r^{2} s^{3} t^{11}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $9$ and $21$ .

Factor $3$ out of $9 r^{2} s^{4} t^{8}$ .

$\frac{3 (3 r^{2} s^{4} t^{8})}{21 r^{2} s^{3} t^{11}}$

Cancel the common factors.

Factor $3$ out of $21 r^{2} s^{3} t^{11}$ .

$\frac{3 (3 r^{2} s^{4} t^{8})}{3 (7 r^{2} s^{3} t^{11})}$

Cancel the common factor.

$\frac{3 (3 r^{2} s^{4} t^{8})}{3 (7 r^{2} s^{3} t^{11})}$

Rewrite the expression.

$\frac{3 r^{2} s^{4} t^{8}}{7 r^{2} s^{3} t^{11}}$

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

$\frac{3 r^{2} s^{4} t^{8}}{7 r^{2} s^{3} t^{11}}$

Rewrite the expression.

$\frac{3 s^{4} t^{8}}{7 s^{3} t^{11}}$

Cancel the common factor of $s^{4}$ and $s^{3}$ .

Factor $s^{3}$ out of $3 s^{4} t^{8}$ .

$\frac{s^{3} (3 s t^{8})}{7 s^{3} t^{11}}$

Cancel the common factors.

Factor $s^{3}$ out of $7 s^{3} t^{11}$ .

$\frac{s^{3} (3 s t^{8})}{s^{3} (7 t^{11})}$

Cancel the common factor.

$\frac{s^{3} (3 s t^{8})}{s^{3} (7 t^{11})}$

Rewrite the expression.

$\frac{3 s t^{8}}{7 t^{11}}$

Cancel the common factor of $t^{8}$ and $t^{11}$ .

Factor $t^{8}$ out of $3 s t^{8}$ .

$\frac{t^{8} (3 s)}{7 t^{11}}$

Cancel the common factors.

Factor $t^{8}$ out of $7 t^{11}$ .

$\frac{t^{8} (3 s)}{t^{8} (7 t^{3})}$

Cancel the common factor.

$\frac{t^{8} (3 s)}{t^{8} (7 t^{3})}$

Rewrite the expression.

$\frac{3 s}{7 t^{3}}$

Simplify ((3rs^2t^4)^2)/(21r^2s^3t^11)

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