Simplify ((5a^2b^3)^0)/((10a^3b^2)^-1)

$\frac{{(5 a^{2} b^{3})}^{0}}{{(10 a^{3} b^{2})}^{- 1}}$

Move ${(10 a^{3} b^{2})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(5 a^{2} b^{3})}^{0} (10 a^{3} b^{2})$

Rewrite using the commutative property of multiplication.

$10 {(5 a^{2} b^{3})}^{0} a^{3} b^{2}$

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

Apply the product rule to $5 a^{2} b^{3}$ .

$10 ({(5 a^{2})}^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Apply the product rule to $5 a^{2}$ .

$10 (5^{0} {(a^{2})}^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Anything raised to $0$ is $1$ .

$10 (1 {(a^{2})}^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Multiply ${(a^{2})}^{0}$ by $1$ .

$10 ({(a^{2})}^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Multiply the exponents in ${(a^{2})}^{0}$ .

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

$10 (a^{2 \cdot 0} {(b^{3})}^{0}) a^{3} b^{2}$

Multiply $2$ by $0$ .

$10 (a^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Multiply $a^{0}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$10 (a^{3} a^{0} {(b^{3})}^{0}) b^{2}$

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

$10 (a^{3 + 0} {(b^{3})}^{0}) b^{2}$

Add $3$ and $0$ .

$10 (a^{3} {(b^{3})}^{0}) b^{2}$

Simplify $10 (a^{3} {(b^{3})}^{0}) b^{2}$ .

$10 a^{3} b^{2}$