Simplify ((2n^(1/3))(3n^(1/3)-4n^(4/3)))/(2n^(-1/3))

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

Step 1

Move

$n^{- \frac{1}{3}}$ to the numerator using the negative exponent rule

$\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Multiply

$n^{\frac{1}{3}}$ by

$n^{\frac{1}{3}}$ by adding the exponents.

Move

$n^{\frac{1}{3}}$ .

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

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 n^{\frac{1}{3} + \frac{1}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})}{2}$

Combine the numerators over the common denominator.

$\frac{2 n^{\frac{1 + 1}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})}{2}$

Add

$1$ and

$1$ .

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

Step 3

Simplify terms.

Cancel the common factor.

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

Divide

$n^{\frac{2}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})$ by

$1$ .

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

Apply the distributive property.

$n^{\frac{2}{3}} (3 n^{\frac{1}{3}}) + n^{\frac{2}{3}} (- 4 n^{\frac{4}{3}})$

Reorder.

Rewrite using the commutative property of multiplication.

$3 n^{\frac{2}{3}} n^{\frac{1}{3}} + n^{\frac{2}{3}} (- 4 n^{\frac{4}{3}})$

Rewrite using the commutative property of multiplication.

$3 n^{\frac{2}{3}} n^{\frac{1}{3}} - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Step 4

Simplify each term.

Multiply

$n^{\frac{2}{3}}$ by

$n^{\frac{1}{3}}$ by adding the exponents.

Move

$n^{\frac{1}{3}}$ .

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

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Combine the numerators over the common denominator.

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

Add

$1$ and

$2$ .

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

Divide

$3$ by

$3$ .

$3 n^{1} - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Simplify

$3 n^{1}$ .

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

Multiply

$n^{\frac{2}{3}}$ by

$n^{\frac{4}{3}}$ by adding the exponents.

Move

$n^{\frac{4}{3}}$ .

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

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 n - 4 n^{\frac{4}{3} + \frac{2}{3}}$

Combine the numerators over the common denominator.

$3 n - 4 n^{\frac{4 + 2}{3}}$

Add

$4$ and

$2$ .

$3 n - 4 n^{\frac{6}{3}}$

Divide

$6$ by

$3$ .

$3 n - 4 n^{2}$

Simplify ((2n^(1/3))(3n^(1/3)-4n^(4/3)))/(2n^(-1/3))

Related Questions