Simplify ((8x^11y^-3)/(4x^5y^-7))^0

${(\frac{8 x^{11} y^{- 3}}{4 x^{5} y^{- 7}})}^{0}$

Step 1

Move $y^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{8 x^{11} y^{- 3} y^{7}}{4 x^{5}})}^{0}$

Step 2

Multiply $y^{- 3}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

${(\frac{8 x^{11} (y^{7} y^{- 3})}{4 x^{5}})}^{0}$

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

${(\frac{8 x^{11} y^{7 - 3}}{4 x^{5}})}^{0}$

Subtract $3$ from $7$ .

${(\frac{8 x^{11} y^{4}}{4 x^{5}})}^{0}$

Step 3

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

Factor $4$ out of $8 x^{11} y^{4}$ .

${(\frac{4 (2 x^{11} y^{4})}{4 x^{5}})}^{0}$

Cancel the common factors.

Factor $4$ out of $4 x^{5}$ .

${(\frac{4 (2 x^{11} y^{4})}{4 (x^{5})})}^{0}$

Cancel the common factor.

${(\frac{4 (2 x^{11} y^{4})}{4 x^{5}})}^{0}$

Rewrite the expression.

${(\frac{2 x^{11} y^{4}}{x^{5}})}^{0}$

Step 4

Cancel the common factor of $x^{11}$ and $x^{5}$ .

Factor $x^{5}$ out of $2 x^{11} y^{4}$ .

${(\frac{x^{5} (2 x^{6} y^{4})}{x^{5}})}^{0}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{x^{5} (2 x^{6} y^{4})}{x^{5} \cdot 1})}^{0}$

Cancel the common factor.

${(\frac{x^{5} (2 x^{6} y^{4})}{x^{5} \cdot 1})}^{0}$

Rewrite the expression.

${(\frac{2 x^{6} y^{4}}{1})}^{0}$

Divide $2 x^{6} y^{4}$ by $1$ .

${(2 x^{6} y^{4})}^{0}$

Step 5

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

Apply the product rule to $2 x^{6} y^{4}$ .

${(2 x^{6})}^{0} {(y^{4})}^{0}$

Apply the product rule to $2 x^{6}$ .

$2^{0} {(x^{6})}^{0} {(y^{4})}^{0}$

Step 6

Anything raised to $0$ is $1$ .

$1 {(x^{6})}^{0} {(y^{4})}^{0}$

Step 7

Multiply ${(x^{6})}^{0}$ by $1$ .

${(x^{6})}^{0} {(y^{4})}^{0}$

Step 8

Multiply the exponents in ${(x^{6})}^{0}$ .

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

$x^{6 \cdot 0} {(y^{4})}^{0}$

Multiply $6$ by $0$ .

$x^{0} {(y^{4})}^{0}$

Step 9

Anything raised to $0$ is $1$ .

$1 {(y^{4})}^{0}$

Step 10

Multiply ${(y^{4})}^{0}$ by $1$ .

${(y^{4})}^{0}$

Step 11

Multiply the exponents in ${(y^{4})}^{0}$ .

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

$y^{4 \cdot 0}$

Multiply $4$ by $0$ .

$y^{0}$

Step 12

Anything raised to $0$ is $1$ .

$1$

Simplify ((8x^11y^-3)/(4x^5y^-7))^0

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