Basic Math Examples

$- 9 m^{5} + \frac{3 m^{- 2} + 3}{{(4 t^{6})}^{- 3}}$

Step 1

To write $- 9 m^{5}$ as a fraction with a common denominator, multiply by $\frac{{(4 t^{6})}^{- 3}}{{(4 t^{6})}^{- 3}}$ .

$- 9 m^{5} \cdot \frac{{(4 t^{6})}^{- 3}}{{(4 t^{6})}^{- 3}} + \frac{3 m^{- 2} + 3}{{(4 t^{6})}^{- 3}}$

Step 2

Combine $- 9 m^{5}$ and $\frac{{(4 t^{6})}^{- 3}}{{(4 t^{6})}^{- 3}}$ .

$\frac{- 9 m^{5} {(4 t^{6})}^{- 3}}{{(4 t^{6})}^{- 3}} + \frac{3 m^{- 2} + 3}{{(4 t^{6})}^{- 3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 9 m^{5} {(4 t^{6})}^{- 3} + 3 m^{- 2} + 3}{{(4 t^{6})}^{- 3}}$

Step 4

Rewrite $\frac{- 9 m^{5} {(4 t^{6})}^{- 3} + 3 m^{- 2} + 3}{{(4 t^{6})}^{- 3}}$ in a factored form.

Tap for more steps...

Step 4.1

Factor $- 3$ out of $- 9 m^{5} {(4 t^{6})}^{- 3} + 3 m^{- 2} + 3$ .

Tap for more steps...

Step 4.1.1

Factor $- 3$ out of $- 9 m^{5} {(4 t^{6})}^{- 3}$ .

$\frac{- 3 (3 m^{5} {(4 t^{6})}^{- 3}) + 3 m^{- 2} + 3}{{(4 t^{6})}^{- 3}}$

Step 4.1.2

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

$\frac{- 3 (3 m^{5} {(4 t^{6})}^{- 3}) - 3 (- m^{- 2}) + 3}{{(4 t^{6})}^{- 3}}$

Step 4.1.3

Factor $- 3$ out of $3$ .

$\frac{- 3 (3 m^{5} {(4 t^{6})}^{- 3}) - 3 (- m^{- 2}) - 3 (- 1)}{{(4 t^{6})}^{- 3}}$

Step 4.1.4

Factor $- 3$ out of $- 3 (3 m^{5} {(4 t^{6})}^{- 3}) - 3 (- m^{- 2})$ .

$\frac{- 3 (3 m^{5} {(4 t^{6})}^{- 3} - m^{- 2}) - 3 (- 1)}{{(4 t^{6})}^{- 3}}$

Step 4.1.5

Factor $- 3$ out of $- 3 (3 m^{5} {(4 t^{6})}^{- 3} - m^{- 2}) - 3 (- 1)$ .

$\frac{- 3 (3 m^{5} {(4 t^{6})}^{- 3} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.2

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

$\frac{- 3 (3 m^{5} \frac{1}{{(4 t^{6})}^{3}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.3

Simplify the denominator.

Tap for more steps...

Step 4.3.1

Apply the product rule to $4 t^{6}$ .

$\frac{- 3 (3 m^{5} \frac{1}{4^{3} {(t^{6})}^{3}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.3.2

Raise $4$ to the power of $3$ .

$\frac{- 3 (3 m^{5} \frac{1}{64 {(t^{6})}^{3}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.3.3

Multiply the exponents in ${(t^{6})}^{3}$ .

Tap for more steps...

Step 4.3.3.1

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

$\frac{- 3 (3 m^{5} \frac{1}{64 t^{6 \cdot 3}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.3.3.2

Multiply $6$ by $3$ .

$\frac{- 3 (3 m^{5} \frac{1}{64 t^{18}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.4

Multiply $3 m^{5} \frac{1}{64 t^{18}}$ .

Tap for more steps...

Step 4.4.1

Combine $3$ and $\frac{1}{64 t^{18}}$ .

$\frac{- 3 (m^{5} \frac{3}{64 t^{18}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.4.2

Combine $m^{5}$ and $\frac{3}{64 t^{18}}$ .

$\frac{- 3 (\frac{m^{5} \cdot 3}{64 t^{18}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.5

Move $3$ to the left of $m^{5}$ .

$\frac{- 3 (\frac{3 \cdot m^{5}}{64 t^{18}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.6

Multiply $3$ by $m^{5}$ .

$\frac{- 3 (\frac{3 m^{5}}{64 t^{18}} - m^{- 2} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.7

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

$\frac{- 3 (\frac{3 m^{5}}{64 t^{18}} - \frac{1}{m^{2}} - 1)}{{(4 t^{6})}^{- 3}}$

Step 4.8

Apply the product rule to $4 t^{6}$ .

$\frac{- 3 (\frac{3 m^{5}}{64 t^{18}} - \frac{1}{m^{2}} - 1)}{4^{- 3} {(t^{6})}^{- 3}}$

Step 4.9

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.9.1

Move $4^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 3 (\frac{3 m^{5}}{64 t^{18}} - \frac{1}{m^{2}} - 1) \cdot 4^{3}}{{(t^{6})}^{- 3}}$

Step 4.9.2

Move ${(t^{6})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$- 3 (\frac{3 m^{5}}{64 t^{18}} - \frac{1}{m^{2}} - 1) \cdot 4^{3} {(t^{6})}^{3}$