Simplify (2/a)^3((4b^3)/(3a))^-4

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

Apply the product rule to $\frac{2}{a}$ .

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

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

$\frac{8}{a^{3}} {(\frac{4 b^{3}}{3 a})}^{- 4}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{8}{a^{3}} {(\frac{3 a}{4 b^{3}})}^{4}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{3 a}{4 b^{3}}$ .

$\frac{8}{a^{3}} \cdot \frac{{(3 a)}^{4}}{{(4 b^{3})}^{4}}$

Apply the product rule to $3 a$ .

$\frac{8}{a^{3}} \cdot \frac{3^{4} a^{4}}{{(4 b^{3})}^{4}}$

Apply the product rule to $4 b^{3}$ .

$\frac{8}{a^{3}} \cdot \frac{3^{4} a^{4}}{4^{4} {(b^{3})}^{4}}$

Simplify terms.

Combine.

$\frac{8 (3^{4} a^{4})}{a^{3} (4^{4} {(b^{3})}^{4})}$

Cancel the common factor of $a^{4}$ and $a^{3}$ .

Factor $a^{3}$ out of $8 (3^{4} a^{4})$ .

$\frac{a^{3} (8 (3^{4} a))}{a^{3} (4^{4} {(b^{3})}^{4})}$

Cancel the common factors.

Cancel the common factor.

$\frac{a^{3} (8 (3^{4} a))}{a^{3} (4^{4} {(b^{3})}^{4})}$

Rewrite the expression.

$\frac{8 (3^{4} a)}{4^{4} {(b^{3})}^{4}}$

Simplify the numerator.

Raise $3$ to the power of $4$ .

$\frac{8 \cdot 81 a}{4^{4} {(b^{3})}^{4}}$

Multiply $8$ by $81$ .

$\frac{648 a}{4^{4} {(b^{3})}^{4}}$

Simplify the denominator.

Raise $4$ to the power of $4$ .

$\frac{648 a}{256 {(b^{3})}^{4}}$

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

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

$\frac{648 a}{256 b^{3 \cdot 4}}$

Multiply $3$ by $4$ .

$\frac{648 a}{256 b^{12}}$

Cancel the common factor of $648$ and $256$ .

Factor $8$ out of $648 a$ .

$\frac{8 (81 a)}{256 b^{12}}$

Cancel the common factors.

Factor $8$ out of $256 b^{12}$ .

$\frac{8 (81 a)}{8 (32 b^{12})}$

Cancel the common factor.

$\frac{8 (81 a)}{8 (32 b^{12})}$

Rewrite the expression.

$\frac{81 a}{32 b^{12}}$

Simplify (2/a)^3((4b^3)/(3a))^-4

Related Questions

Support LCMGCF.com by disabling your adblocker.