Simplify ((4x^3)^3)/((8x^-1)^4)

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

Step 1

Simplify the numerator.

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

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

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

$\frac{64 {(x^{3})}^{3}}{{(8 x^{- 1})}^{4}}$

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

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

$\frac{64 x^{3 \cdot 3}}{{(8 x^{- 1})}^{4}}$

Multiply $3$ by $3$ .

$\frac{64 x^{9}}{{(8 x^{- 1})}^{4}}$

Step 2

Simplify the denominator.

Apply the product rule to $8 x^{- 1}$ .

$\frac{64 x^{9}}{8^{4} {(x^{- 1})}^{4}}$

Raise $8$ to the power of $4$ .

$\frac{64 x^{9}}{4096 {(x^{- 1})}^{4}}$

Multiply the exponents in ${(x^{- 1})}^{4}$ .

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

$\frac{64 x^{9}}{4096 x^{- 1 \cdot 4}}$

Multiply $- 1$ by $4$ .

$\frac{64 x^{9}}{4096 x^{- 4}}$

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

$\frac{64 x^{9}}{4096 \frac{1}{x^{4}}}$

Step 3

Combine $4096$ and $\frac{1}{x^{4}}$ .

$\frac{64 x^{9}}{\frac{4096}{x^{4}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$64 x^{9} \frac{x^{4}}{4096}$

Step 5

Cancel the common factor of $64$ .

Factor $64$ out of $64 x^{9}$ .

$64 (x^{9}) \frac{x^{4}}{4096}$

Factor $64$ out of $4096$ .

$64 (x^{9}) \frac{x^{4}}{64 (64)}$

Cancel the common factor.

$64 x^{9} \frac{x^{4}}{64 \cdot 64}$

Rewrite the expression.

$x^{9} \frac{x^{4}}{64}$

Step 6

Combine $x^{9}$ and $\frac{x^{4}}{64}$ .

$\frac{x^{9} x^{4}}{64}$

Step 7

Multiply $x^{9}$ by $x^{4}$ by adding the exponents.

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

$\frac{x^{9 + 4}}{64}$

Add $9$ and $4$ .

$\frac{x^{13}}{64}$

Simplify ((4x^3)^3)/((8x^-1)^4)

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