Simplify ((b^2)/(-2b^5*ab^2))^0

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

Step 1

Multiply $b^{5}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

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

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

${(\frac{b^{2}}{- 2 b^{2 + 5} \cdot a})}^{0}$

Add $2$ and $5$ .

${(\frac{b^{2}}{- 2 b^{7} \cdot a})}^{0}$

Step 2

Cancel the common factor of $b^{2}$ and $b^{7}$ .

Multiply by $1$ .

${(\frac{b^{2} \cdot 1}{- 2 b^{7} \cdot a})}^{0}$

Cancel the common factors.

Factor $b^{2}$ out of $- 2 b^{7} \cdot a$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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

Apply the product rule to $- \frac{1}{2 b^{5} a}$ .

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

Apply the product rule to $\frac{1}{2 b^{5} a}$ .

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

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

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

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

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

Step 5

Simplify the expression.

Anything raised to $0$ is $1$ .

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

Multiply $\frac{1^{0}}{2^{0} {(b^{5})}^{0} a^{0}}$ by $1$ .

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

Anything raised to $0$ is $1$ .

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

Step 6

Simplify the denominator.

Anything raised to $0$ is $1$ .

$\frac{1}{1 {(b^{5})}^{0} a^{0}}$

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

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

$\frac{1}{1 b^{5 \cdot 0} a^{0}}$

Multiply $5$ by $0$ .

$\frac{1}{1 b^{0} a^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{1 \cdot 1 a^{0}}$

Anything raised to $0$ is $1$ .

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

Combine exponents.

Multiply $1$ by $1$ .

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

Multiply $1$ by $1$ .

$\frac{1}{1}$

Step 7

Divide $1$ by $1$ .

$1$

Simplify ((b^2)/(-2b^5*ab^2))^0

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