Algebra Examples

$\frac{{(2 y^{- 5} n^{4})}^{- 3}}{6 y^{7} n^{- 5}}$

Step 1

Move ${(2 y^{- 5} n^{4})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{6 y^{7} n^{- 5} {(2 y^{- 5} n^{4})}^{3}}$

Step 2

Move $n^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{n^{5}}{6 y^{7} {(2 y^{- 5} n^{4})}^{3}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Apply the product rule to $2 y^{- 5} n^{4}$ .

$\frac{n^{5}}{6 y^{7} {(2 y^{- 5})}^{3} {(n^{4})}^{3}}$

Step 3.2

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

$\frac{n^{5}}{6 y^{7} {(2 \frac{1}{y^{5}})}^{3} {(n^{4})}^{3}}$

Step 3.3

Combine $2$ and $\frac{1}{y^{5}}$ .

$\frac{n^{5}}{6 y^{7} {(\frac{2}{y^{5}})}^{3} {(n^{4})}^{3}}$

Step 3.4

Apply the product rule to $\frac{2}{y^{5}}$ .

$\frac{n^{5}}{6 y^{7} \frac{2^{3}}{{(y^{5})}^{3}} {(n^{4})}^{3}}$

Step 3.5

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

$\frac{n^{5}}{6 y^{7} \frac{8}{{(y^{5})}^{3}} {(n^{4})}^{3}}$

Step 3.6

Multiply the exponents in ${(y^{5})}^{3}$ .

Tap for more steps...

Step 3.6.1

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

$\frac{n^{5}}{6 y^{7} \frac{8}{y^{5 \cdot 3}} {(n^{4})}^{3}}$

Step 3.6.2

Multiply $5$ by $3$ .

$\frac{n^{5}}{6 y^{7} \frac{8}{y^{15}} {(n^{4})}^{3}}$

Step 3.7

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

Tap for more steps...

Step 3.7.1

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

$\frac{n^{5}}{6 y^{7} \frac{8}{y^{15}} n^{4 \cdot 3}}$

Step 3.7.2

Multiply $4$ by $3$ .

$\frac{n^{5}}{6 y^{7} \frac{8}{y^{15}} n^{12}}$

Step 3.8

Combine exponents.

Tap for more steps...

Step 3.8.1

Combine $6$ and $\frac{8}{y^{15}}$ .

$\frac{n^{5}}{y^{7} \frac{6 \cdot 8}{y^{15}} n^{12}}$

Step 3.8.2

Multiply $6$ by $8$ .

$\frac{n^{5}}{y^{7} \frac{48}{y^{15}} n^{12}}$

Step 3.8.3

Combine $y^{7}$ and $\frac{48}{y^{15}}$ .

$\frac{n^{5}}{\frac{y^{7} \cdot 48}{y^{15}} n^{12}}$

Step 3.8.4

Combine $\frac{y^{7} \cdot 48}{y^{15}}$ and $n^{12}$ .

$\frac{n^{5}}{\frac{y^{7} \cdot 48 n^{12}}{y^{15}}}$

Step 3.9

Reduce the expression $\frac{y^{7} \cdot 48 n^{12}}{y^{15}}$ by cancelling the common factors.

Tap for more steps...

Step 3.9.1

Factor $y^{7}$ out of $y^{7} \cdot 48 n^{12}$ .

$\frac{n^{5}}{\frac{y^{7} (48 n^{12})}{y^{15}}}$

Step 3.9.2

Factor $y^{7}$ out of $y^{15}$ .

$\frac{n^{5}}{\frac{y^{7} (48 n^{12})}{y^{7} y^{8}}}$

Step 3.9.3

Cancel the common factor.

$\frac{n^{5}}{\frac{y^{7} (48 n^{12})}{y^{7} y^{8}}}$

Step 3.9.4

Rewrite the expression.

$\frac{n^{5}}{\frac{48 n^{12}}{y^{8}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$n^{5} \frac{y^{8}}{48 n^{12}}$

Step 5

Cancel the common factor of $n^{5}$ .

Tap for more steps...

Step 5.1

Factor $n^{5}$ out of $48 n^{12}$ .

$n^{5} \frac{y^{8}}{n^{5} (48 n^{7})}$

Step 5.2

Cancel the common factor.

$n^{5} \frac{y^{8}}{n^{5} (48 n^{7})}$

Step 5.3

Rewrite the expression.

$\frac{y^{8}}{48 n^{7}}$