Algebra Examples

$\frac{3 m^{8}}{{(4 m t^{- 2})}^{2}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Apply the product rule to $4 m t^{- 2}$ .

$\frac{3 m^{8}}{{(4 m)}^{2} {(t^{- 2})}^{2}}$

Step 1.2

Apply the product rule to $4 m$ .

$\frac{3 m^{8}}{4^{2} m^{2} {(t^{- 2})}^{2}}$

Step 1.3

Raise $4$ to the power of $2$ .

$\frac{3 m^{8}}{16 m^{2} {(t^{- 2})}^{2}}$

Step 1.4

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

Tap for more steps...

Step 1.4.1

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

$\frac{3 m^{8}}{16 m^{2} t^{- 2 \cdot 2}}$

Step 1.4.2

Multiply $- 2$ by $2$ .

$\frac{3 m^{8}}{16 m^{2} t^{- 4}}$

Step 1.5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 m^{8}}{16 m^{2} \frac{1}{t^{4}}}$

Step 1.6

Combine exponents.

Tap for more steps...

Step 1.6.1

Combine $16$ and $\frac{1}{t^{4}}$ .

$\frac{3 m^{8}}{m^{2} \frac{16}{t^{4}}}$

Step 1.6.2

Combine $m^{2}$ and $\frac{16}{t^{4}}$ .

$\frac{3 m^{8}}{\frac{m^{2} \cdot 16}{t^{4}}}$

Step 1.7

Move $16$ to the left of $m^{2}$ .

$\frac{3 m^{8}}{\frac{16 m^{2}}{t^{4}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$3 m^{8} \frac{t^{4}}{16 m^{2}}$

Step 3

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

Tap for more steps...

Step 3.1

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

$m^{2} (3 m^{6}) \frac{t^{4}}{16 m^{2}}$

Step 3.2

Factor $m^{2}$ out of $16 m^{2}$ .

$m^{2} (3 m^{6}) \frac{t^{4}}{m^{2} \cdot 16}$

Step 3.3

Cancel the common factor.

$m^{2} (3 m^{6}) \frac{t^{4}}{m^{2} \cdot 16}$

Step 3.4

Rewrite the expression.

$3 m^{6} \frac{t^{4}}{16}$

Step 4

Combine $3$ and $\frac{t^{4}}{16}$ .

$m^{6} \frac{3 t^{4}}{16}$

Step 5

Combine $m^{6}$ and $\frac{3 t^{4}}{16}$ .

$\frac{m^{6} (3 t^{4})}{16}$

Step 6

Move $3$ to the left of $m^{6}$ .

$\frac{3 m^{6} t^{4}}{16}$