Simplify ((2hj^2k^-2*h^4j^-1k^4)^0)/(2h^-3j^-4k^-2)

$\frac{{(2 h j^{2} k^{- 2} \cdot h^{4} j^{- 1} k^{4})}^{0}}{2 h^{- 3} j^{- 4} k^{- 2}}$

Step 1

Move $h^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(2 h j^{2} k^{- 2} \cdot (h^{4} j^{- 1} k^{4}))}^{0} h^{3}}{2 j^{- 4} k^{- 2}}$

Step 2

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

$\frac{{(2 h j^{2} k^{- 2} \cdot (h^{4} j^{- 1} k^{4}))}^{0} h^{3} j^{4}}{2 k^{- 2}}$

Step 3

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

$\frac{{(2 h j^{2} k^{- 2} \cdot (h^{4} j^{- 1} k^{4}))}^{0} h^{3} j^{4} k^{2}}{2}$

Step 4

Simplify the numerator.

Multiply $h$ by $h^{4}$ by adding the exponents.

Move $h^{4}$ .

$\frac{{(2 (h^{4} h) j^{2} k^{- 2} \cdot (j^{- 1} k^{4}))}^{0} h^{3} j^{4} k^{2}}{2}$

Multiply $h^{4}$ by $h$ .

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

$\frac{{(2 (h^{4} h^{1}) j^{2} k^{- 2} \cdot (j^{- 1} k^{4}))}^{0} h^{3} j^{4} k^{2}}{2}$

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

$\frac{{(2 h^{4 + 1} j^{2} k^{- 2} \cdot (j^{- 1} k^{4}))}^{0} h^{3} j^{4} k^{2}}{2}$

Add $4$ and $1$ .

$\frac{{(2 h^{5} j^{2} k^{- 2} \cdot (j^{- 1} k^{4}))}^{0} h^{3} j^{4} k^{2}}{2}$

Multiply $j^{2}$ by $j^{- 1}$ by adding the exponents.

Move $j^{- 1}$ .

$\frac{{(2 h^{5} (j^{- 1} j^{2}) k^{- 2} \cdot k^{4})}^{0} h^{3} j^{4} k^{2}}{2}$

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

$\frac{{(2 h^{5} j^{- 1 + 2} k^{- 2} \cdot k^{4})}^{0} h^{3} j^{4} k^{2}}{2}$

Add $- 1$ and $2$ .

$\frac{{(2 h^{5} j^{1} k^{- 2} \cdot k^{4})}^{0} h^{3} j^{4} k^{2}}{2}$

Simplify $2 h^{5} j^{1} k^{- 2} \cdot k^{4}$ .

$\frac{{(2 h^{5} j k^{- 2} \cdot k^{4})}^{0} h^{3} j^{4} k^{2}}{2}$

Multiply $k^{- 2}$ by $k^{4}$ by adding the exponents.

Move $k^{4}$ .

$\frac{{(2 h^{5} j (k^{4} k^{- 2}))}^{0} h^{3} j^{4} k^{2}}{2}$

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

$\frac{{(2 h^{5} j k^{4 - 2})}^{0} h^{3} j^{4} k^{2}}{2}$

Subtract $2$ from $4$ .

$\frac{{(2 h^{5} j k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

Step 5

Simplify the numerator.

Apply the product rule to $2 h^{5} j k^{2}$ .

$\frac{{(2 h^{5} j)}^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

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

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

$\frac{{(2 h^{5})}^{0} j^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

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

$\frac{2^{0} {(h^{5})}^{0} j^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

Anything raised to $0$ is $1$ .

$\frac{1 {(h^{5})}^{0} j^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

Multiply ${(h^{5})}^{0}$ by $1$ .

$\frac{{(h^{5})}^{0} j^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

Multiply the exponents in ${(h^{5})}^{0}$ .

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

$\frac{h^{5 \cdot 0} j^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

Multiply $5$ by $0$ .

$\frac{h^{0} j^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

Anything raised to $0$ is $1$ .

$\frac{1 j^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

Multiply $j^{0}$ by $1$ .

$\frac{j^{0} {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

Anything raised to $0$ is $1$ .

$\frac{1 {(k^{2})}^{0} h^{3} j^{4} k^{2}}{2}$

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

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

$\frac{1 k^{2 \cdot 0} h^{3} j^{4} k^{2}}{2}$

Multiply $2$ by $0$ .

$\frac{1 k^{0} h^{3} j^{4} k^{2}}{2}$

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1 h^{3} j^{4} k^{2}}{2}$

Combine exponents.

Multiply $1$ by $1$ .

$\frac{1 h^{3} j^{4} k^{2}}{2}$

Multiply $h^{3}$ by $1$ .

$\frac{h^{3} j^{4} k^{2}}{2}$

Simplify ((2hj^2k^-2*h^4j^-1k^4)^0)/(2h^-3j^-4k^-2)

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