Simplify (16^-2a^-4b^0)/((2a^2b)^-5)

$\frac{16^{- 2} a^{- 4} b^{0}}{{(2 a^{2} b)}^{- 5}}$

Step 1

Simplify the expression.

Move $16^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{a^{- 4}}{{(2 a^{2} b)}^{- 5} \cdot 16^{2}}$

Move $a^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(2 a^{2} b)}^{- 5} \cdot 16^{2} a^{4}}$

Move ${(2 a^{2} b)}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(2 a^{2} b)}^{5}}{16^{2} a^{4}}$

Step 2

Simplify the numerator.

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

$\frac{{(2 a^{2})}^{5} b^{5}}{16^{2} a^{4}}$

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

$\frac{2^{5} {(a^{2})}^{5} b^{5}}{16^{2} a^{4}}$

Raise $2$ to the power of $5$ .

$\frac{32 {(a^{2})}^{5} b^{5}}{16^{2} a^{4}}$

Multiply the exponents in ${(a^{2})}^{5}$ .

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

$\frac{32 a^{2 \cdot 5} b^{5}}{16^{2} a^{4}}$

Multiply $2$ by $5$ .

$\frac{32 a^{10} b^{5}}{16^{2} a^{4}}$

Step 3

Reduce the expression by cancelling the common factors.

Raise $16$ to the power of $2$ .

$\frac{32 a^{10} b^{5}}{256 a^{4}}$

Cancel the common factor of $32$ and $256$ .

Factor $32$ out of $32 a^{10} b^{5}$ .

$\frac{32 (a^{10} b^{5})}{256 a^{4}}$

Cancel the common factors.

Factor $32$ out of $256 a^{4}$ .

$\frac{32 (a^{10} b^{5})}{32 (8 a^{4})}$

Cancel the common factor.

$\frac{32 (a^{10} b^{5})}{32 (8 a^{4})}$

Rewrite the expression.

$\frac{a^{10} b^{5}}{8 a^{4}}$

Cancel the common factor of $a^{10}$ and $a^{4}$ .

Factor $a^{4}$ out of $a^{10} b^{5}$ .

$\frac{a^{4} (a^{6} b^{5})}{8 a^{4}}$

Cancel the common factors.

Factor $a^{4}$ out of $8 a^{4}$ .

$\frac{a^{4} (a^{6} b^{5})}{a^{4} \cdot 8}$

Cancel the common factor.

$\frac{a^{4} (a^{6} b^{5})}{a^{4} \cdot 8}$

Rewrite the expression.

$\frac{a^{6} b^{5}}{8}$

Simplify (16^-2a^-4b^0)/((2a^2b)^-5)

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