Simplify (4c^2-3c)/(c^(-2/3))

$\frac{4 c^{2} - 3 c}{c^{- \frac{2}{3}}}$

Step 1

Move $c^{- \frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Apply the distributive property.

$4 c^{2} c^{\frac{2}{3}} - 3 c \cdot c^{\frac{2}{3}}$

Step 3

Multiply $c^{2}$ by $c^{\frac{2}{3}}$ by adding the exponents.

Move $c^{\frac{2}{3}}$ .

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

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

$4 c^{\frac{2}{3} + 2} - 3 c \cdot c^{\frac{2}{3}}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 c^{\frac{2}{3} + 2 \cdot \frac{3}{3}} - 3 c \cdot c^{\frac{2}{3}}$

Combine $2$ and $\frac{3}{3}$ .

$4 c^{\frac{2}{3} + \frac{2 \cdot 3}{3}} - 3 c \cdot c^{\frac{2}{3}}$

Combine the numerators over the common denominator.

$4 c^{\frac{2 + 2 \cdot 3}{3}} - 3 c \cdot c^{\frac{2}{3}}$

Simplify the numerator.

Multiply $2$ by $3$ .

$4 c^{\frac{2 + 6}{3}} - 3 c \cdot c^{\frac{2}{3}}$

Add $2$ and $6$ .

$4 c^{\frac{8}{3}} - 3 c \cdot c^{\frac{2}{3}}$

Step 4

Multiply $c$ by $c^{\frac{2}{3}}$ by adding the exponents.

Move $c^{\frac{2}{3}}$ .

$4 c^{\frac{8}{3}} - 3 (c^{\frac{2}{3}} c)$

Multiply $c^{\frac{2}{3}}$ by $c$ .

Raise $c$ to the power of $1$ .

$4 c^{\frac{8}{3}} - 3 (c^{\frac{2}{3}} c^{1})$

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

$4 c^{\frac{8}{3}} - 3 c^{\frac{2}{3} + 1}$

Write $1$ as a fraction with a common denominator.

$4 c^{\frac{8}{3}} - 3 c^{\frac{2}{3} + \frac{3}{3}}$

Combine the numerators over the common denominator.

$4 c^{\frac{8}{3}} - 3 c^{\frac{2 + 3}{3}}$

Add $2$ and $3$ .

$4 c^{\frac{8}{3}} - 3 c^{\frac{5}{3}}$