Write the Fraction in Simplest Form ((2t)^2)/(3t^8)

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

Step 1

Simplify the numerator.

Apply the product rule to $2 t$ .

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

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

$\frac{4 t^{2}}{3 t^{8}}$

$\frac{4 t^{2}}{3 t^{8}}$

Step 2

Cancel the common factor of $t^{2}$ and $t^{8}$ .

Factor $t^{2}$ out of $4 t^{2}$ .

$\frac{t^{2} \cdot 4}{3 t^{8}}$

Cancel the common factors.

Factor $t^{2}$ out of $3 t^{8}$ .

$\frac{t^{2} \cdot 4}{t^{2} (3 t^{6})}$

Cancel the common factor.

$\frac{t^{2} \cdot 4}{t^{2} (3 t^{6})}$

Rewrite the expression.

$\frac{4}{3 t^{6}}$

$\frac{4}{3 t^{6}}$

$\frac{4}{3 t^{6}}$

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