Simplify ((4m^2n^2)/(8m^-1l))^0

${(\frac{4 m^{2} n^{2}}{8 m^{- 1} l})}^{0}$

Move $m^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{4 m^{2} n^{2} m}{8 l})}^{0}$

Multiply $m^{2}$ by $m$ by adding the exponents.

Move $m$ .

${(\frac{4 (m \cdot m^{2}) n^{2}}{8 l})}^{0}$

Multiply $m$ by $m^{2}$ .

Raise $m$ to the power of $1$ .

${(\frac{4 (m^{1} m^{2}) n^{2}}{8 l})}^{0}$

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

${(\frac{4 m^{1 + 2} n^{2}}{8 l})}^{0}$

Add $1$ and $2$ .

${(\frac{4 m^{3} n^{2}}{8 l})}^{0}$

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 m^{3} n^{2}$ .

${(\frac{4 (m^{3} n^{2})}{8 l})}^{0}$

Cancel the common factors.

Factor $4$ out of $8 l$ .

${(\frac{4 (m^{3} n^{2})}{4 (2 l)})}^{0}$

Cancel the common factor.

${(\frac{4 (m^{3} n^{2})}{4 (2 l)})}^{0}$

Rewrite the expression.

${(\frac{m^{3} n^{2}}{2 l})}^{0}$

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

Apply the product rule to $\frac{m^{3} n^{2}}{2 l}$ .

$\frac{{(m^{3} n^{2})}^{0}}{{(2 l)}^{0}}$

Apply the product rule to $m^{3} n^{2}$ .

$\frac{{(m^{3})}^{0} {(n^{2})}^{0}}{{(2 l)}^{0}}$

Apply the product rule to $2 l$ .

$\frac{{(m^{3})}^{0} {(n^{2})}^{0}}{2^{0} l^{0}}$

Simplify the numerator.

Multiply the exponents in ${(m^{3})}^{0}$ .

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

$\frac{m^{3 \cdot 0} {(n^{2})}^{0}}{2^{0} l^{0}}$

Multiply $3$ by $0$ .

$\frac{m^{0} {(n^{2})}^{0}}{2^{0} l^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 {(n^{2})}^{0}}{2^{0} l^{0}}$

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

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

$\frac{1 n^{2 \cdot 0}}{2^{0} l^{0}}$

Multiply $2$ by $0$ .

$\frac{1 n^{0}}{2^{0} l^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{2^{0} l^{0}}$

Multiply $1$ by $1$ .

$\frac{1}{2^{0} l^{0}}$

Simplify the denominator.

Anything raised to $0$ is $1$ .

$\frac{1}{1 l^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{1 \cdot 1}$

Multiply $1$ by $1$ .

$\frac{1}{1}$

Divide $1$ by $1$ .

$1$

Simplify ((4m^2n^2)/(8m^-1l))^0

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