Finite Math Examples

${(2 x^{2})}^{3 - 2 m} {(\frac{1}{x})}^{2 m}$

Step 1

Apply the product rule to $2 x^{2}$ .

$2^{3 - 2 m} {(x^{2})}^{3 - 2 m} {(\frac{1}{x})}^{2 m}$

Step 2

Multiply the exponents in ${(x^{2})}^{3 - 2 m}$ .

Tap for more steps...

Step 2.1

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

$2^{3 - 2 m} x^{2 (3 - 2 m)} {(\frac{1}{x})}^{2 m}$

Step 2.2

Apply the distributive property.

$2^{3 - 2 m} x^{2 \cdot 3 + 2 (- 2 m)} {(\frac{1}{x})}^{2 m}$

Step 2.3

Multiply $2$ by $3$ .

$2^{3 - 2 m} x^{6 + 2 (- 2 m)} {(\frac{1}{x})}^{2 m}$

Step 2.4

Multiply $- 2$ by $2$ .

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

Step 3

Apply the product rule to $\frac{1}{x}$ .

$2^{3 - 2 m} x^{6 - 4 m} \frac{1^{2 m}}{x^{2 m}}$

Step 4

One to any power is one.

$2^{3 - 2 m} x^{6 - 4 m} \frac{1}{x^{2 m}}$

Step 5

Multiply $2^{3 - 2 m} x^{6 - 4 m} \frac{1}{x^{2 m}}$ .

Tap for more steps...

Step 5.1

Combine $2^{3 - 2 m}$ and $\frac{1}{x^{2 m}}$ .

$x^{6 - 4 m} \frac{2^{3 - 2 m}}{x^{2 m}}$

Step 5.2

Combine $x^{6 - 4 m}$ and $\frac{2^{3 - 2 m}}{x^{2 m}}$ .

$\frac{x^{6 - 4 m} \cdot 2^{3 - 2 m}}{x^{2 m}}$

Step 6

Cancel the common factor of $x^{6 - 4 m}$ and $x^{2 m}$ .

Tap for more steps...

Step 6.1

Factor $x^{2 m}$ out of $x^{6 - 4 m} \cdot 2^{3 - 2 m}$ .

$\frac{x^{2 m} (x^{6 - 6 m} \cdot 2^{3 - 2 m})}{x^{2 m}}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Multiply by $1$ .

$\frac{x^{2 m} (x^{6 - 6 m} \cdot 2^{3 - 2 m})}{x^{2 m} \cdot 1}$

Step 6.2.2

Cancel the common factor.

$\frac{x^{2 m} (x^{6 - 6 m} \cdot 2^{3 - 2 m})}{x^{2 m} \cdot 1}$

Step 6.2.3

Rewrite the expression.

$\frac{x^{6 - 6 m} \cdot 2^{3 - 2 m}}{1}$

Step 6.2.4

Divide $x^{6 - 6 m} \cdot 2^{3 - 2 m}$ by $1$ .

$x^{6 - 6 m} \cdot 2^{3 - 2 m}$