Simplify ba^4*(2ba^4)^-3

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

Step 1

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

$b a^{4} \cdot \frac{1}{{(2 b a^{4})}^{3}}$

Step 2

Simplify the denominator.

Apply the product rule to $2 b a^{4}$ .

$b a^{4} \cdot \frac{1}{{(2 b)}^{3} {(a^{4})}^{3}}$

Apply the product rule to $2 b$ .

$b a^{4} \cdot \frac{1}{2^{3} b^{3} {(a^{4})}^{3}}$

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

$b a^{4} \cdot \frac{1}{8 b^{3} {(a^{4})}^{3}}$

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

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

$b a^{4} \cdot \frac{1}{8 b^{3} a^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$b a^{4} \cdot \frac{1}{8 b^{3} a^{12}}$

Step 3

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

Factor $b a^{4}$ out of $8 b^{3} a^{12}$ .

$b a^{4} \cdot \frac{1}{b a^{4} (8 b^{2} a^{8})}$

Cancel the common factor.

$b a^{4} \cdot \frac{1}{b a^{4} (8 b^{2} a^{8})}$

Rewrite the expression.

$\frac{1}{8 b^{2} a^{8}}$