Algebra Examples

$- \frac{6 j^{- 9}}{{(- 2 j^{4})}^{3}}$

Step 1

Move $j^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{6}{{(- 2 j^{4})}^{3} j^{9}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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

$- \frac{6}{{(- 2)}^{3} {(j^{4})}^{3} j^{9}}$

Step 2.2

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

$- \frac{6}{- 8 {(j^{4})}^{3} j^{9}}$

Step 2.3

Multiply the exponents in ${(j^{4})}^{3}$ .

Tap for more steps...

Step 2.3.1

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

$- \frac{6}{- 8 j^{4 \cdot 3} j^{9}}$

Step 2.3.2

Multiply $4$ by $3$ .

$- \frac{6}{- 8 j^{12} j^{9}}$

Step 2.4

Multiply $j^{12}$ by $j^{9}$ by adding the exponents.

Tap for more steps...

Step 2.4.1

Move $j^{9}$ .

$- \frac{6}{- 8 (j^{9} j^{12})}$

Step 2.4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{6}{- 8 j^{9 + 12}}$

Step 2.4.3

Add $9$ and $12$ .

$- \frac{6}{- 8 j^{21}}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor of $6$ and $- 8$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $6$ .

$- \frac{2 (3)}{- 8 j^{21}}$

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Factor $2$ out of $- 8 j^{21}$ .

$- \frac{2 (3)}{2 (- 4 j^{21})}$

Step 3.1.2.2

Cancel the common factor.

$- \frac{2 \cdot 3}{2 (- 4 j^{21})}$

Step 3.1.2.3

Rewrite the expression.

$- \frac{3}{- 4 j^{21}}$

Step 3.2

Move the negative in front of the fraction.

$- - \frac{3}{4 j^{21}}$

Step 4

Multiply $- - \frac{3}{4 j^{21}}$ .

Tap for more steps...

Step 4.1

Multiply $- 1$ by $- 1$ .

$1 \frac{3}{4 j^{21}}$

Step 4.2

Multiply $\frac{3}{4 j^{21}}$ by $1$ .

$\frac{3}{4 j^{21}}$