Algebra Examples

$7 x {(- 7 x + 1)}^{- \frac{2}{3}} - 2 {(- 7 x + 1)}^{\frac{1}{3}}$

Step 1

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

$7 x \frac{1}{{(- 7 x + 1)}^{\frac{2}{3}}} - 2 {(- 7 x + 1)}^{\frac{1}{3}}$

Step 2

Multiply $7 x \frac{1}{{(- 7 x + 1)}^{\frac{2}{3}}}$ .

Tap for more steps...

Step 2.1

Combine $7$ and $\frac{1}{{(- 7 x + 1)}^{\frac{2}{3}}}$ .

$x \frac{7}{{(- 7 x + 1)}^{\frac{2}{3}}} - 2 {(- 7 x + 1)}^{\frac{1}{3}}$

Step 2.2

Combine $x$ and $\frac{7}{{(- 7 x + 1)}^{\frac{2}{3}}}$ .

$\frac{x \cdot 7}{{(- 7 x + 1)}^{\frac{2}{3}}} - 2 {(- 7 x + 1)}^{\frac{1}{3}}$

Step 3

Move $7$ to the left of $x$ .

$\frac{7 \cdot x}{{(- 7 x + 1)}^{\frac{2}{3}}} - 2 {(- 7 x + 1)}^{\frac{1}{3}}$

Step 4

Multiply $7$ by $x$ .

$\frac{7 x}{{(- 7 x + 1)}^{\frac{2}{3}}} - 2 {(- 7 x + 1)}^{\frac{1}{3}}$

Step 5

To write $- 2 {(- 7 x + 1)}^{\frac{1}{3}}$ as a fraction with a common denominator, multiply by $\frac{{(- 7 x + 1)}^{\frac{2}{3}}}{{(- 7 x + 1)}^{\frac{2}{3}}}$ .

$\frac{7 x}{{(- 7 x + 1)}^{\frac{2}{3}}} - 2 {(- 7 x + 1)}^{\frac{1}{3}} \cdot \frac{{(- 7 x + 1)}^{\frac{2}{3}}}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 6

Combine $- 2 {(- 7 x + 1)}^{\frac{1}{3}}$ and $\frac{{(- 7 x + 1)}^{\frac{2}{3}}}{{(- 7 x + 1)}^{\frac{2}{3}}}$ .

$\frac{7 x}{{(- 7 x + 1)}^{\frac{2}{3}}} + \frac{- 2 {(- 7 x + 1)}^{\frac{1}{3}} {(- 7 x + 1)}^{\frac{2}{3}}}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 7

Combine the numerators over the common denominator.

$\frac{7 x - 2 {(- 7 x + 1)}^{\frac{1}{3}} {(- 7 x + 1)}^{\frac{2}{3}}}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 8

Reorder terms.

$\frac{- 2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}} + 7 x}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9

Rewrite $\frac{- 2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}} + 7 x}{{(- 7 x + 1)}^{\frac{2}{3}}}$ in a factored form.

Tap for more steps...

Step 9.1

Factor $- 1$ out of $- 2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}} + 7 x$ .

Tap for more steps...

Step 9.1.1

Reorder $- 2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}}$ and $7 x$ .

$\frac{7 x - 2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}}}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.1.2

Factor $- 1$ out of $7 x$ .

$\frac{- (- 7 x) - 2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}}}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.1.3

Factor $- 1$ out of $- 2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}}$ .

$\frac{- (- 7 x) - (2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}})}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.1.4

Factor $- 1$ out of $- (- 7 x) - (2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}})$ .

$\frac{- (- 7 x + 2 {(- 7 x + 1)}^{\frac{2}{3}} {(- 7 x + 1)}^{\frac{1}{3}})}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.2

Multiply ${(- 7 x + 1)}^{\frac{2}{3}}$ by ${(- 7 x + 1)}^{\frac{1}{3}}$ by adding the exponents.

Tap for more steps...

Step 9.2.1

Move ${(- 7 x + 1)}^{\frac{1}{3}}$ .

$\frac{- (- 7 x + 2 ({(- 7 x + 1)}^{\frac{1}{3}} {(- 7 x + 1)}^{\frac{2}{3}}))}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.2.2

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

$\frac{- (- 7 x + 2 {(- 7 x + 1)}^{\frac{1}{3} + \frac{2}{3}})}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.2.3

Combine the numerators over the common denominator.

$\frac{- (- 7 x + 2 {(- 7 x + 1)}^{\frac{1 + 2}{3}})}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.2.4

Add $1$ and $2$ .

$\frac{- (- 7 x + 2 {(- 7 x + 1)}^{\frac{3}{3}})}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.2.5

Divide $3$ by $3$ .

$\frac{- (- 7 x + 2 {(- 7 x + 1)}^{1})}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.3

Simplify $2 {(- 7 x + 1)}^{1}$ .

$\frac{- (- 7 x + 2 (- 7 x + 1))}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.4

Apply the distributive property.

$\frac{- (- 7 x + 2 (- 7 x) + 2 \cdot 1)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.5

Multiply $- 7$ by $2$ .

$\frac{- (- 7 x - 14 x + 2 \cdot 1)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.6

Multiply $2$ by $1$ .

$\frac{- (- 7 x - 14 x + 2)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 9.7

Subtract $14 x$ from $- 7 x$ .

$\frac{- (- 21 x + 2)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 10

Factor.

Tap for more steps...

Step 10.1

Factor $- 1$ out of $- 21 x + 2$ .

Tap for more steps...

Step 10.1.1

Factor $- 1$ out of $- 21 x$ .

$\frac{- (- (21 x) + 2)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 10.1.2

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{- (- (21 x) - 1 (- 2))}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 10.1.3

Factor $- 1$ out of $- (21 x) - 1 (- 2)$ .

$\frac{- - (21 x - 2)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 10.2

Remove unnecessary parentheses.

$\frac{- - 1 (21 x - 2)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 11

Combine exponents.

Tap for more steps...

Step 11.1

Factor out negative.

$\frac{- - (21 x - 2)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 11.2

Multiply $- 1$ by $- 1$ .

$\frac{1 (21 x - 2)}{{(- 7 x + 1)}^{\frac{2}{3}}}$

Step 11.3

Multiply $21 x - 2$ by $1$ .

$\frac{21 x - 2}{{(- 7 x + 1)}^{\frac{2}{3}}}$