Simplify -(-5a^-2bc)^0

$- {(- 5 a^{- 2} b c)}^{0}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Combine $- 5$ and $\frac{1}{a^{2}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Combine $b$ and $\frac{5}{a^{2}}$ .

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

Step 5

Move $5$ to the left of $b$ .

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

Step 6

Combine $c$ and $\frac{5 b}{a^{2}}$ .

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

Step 7

Move $5$ to the left of $c$ .

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

Step 8

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

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

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

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

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

Apply the product rule to $5 c b$ .

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

Apply the product rule to $5 c$ .

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

Step 9

Multiply $- 1$ by ${(- 1)}^{0}$ by adding the exponents.

Move ${(- 1)}^{0}$ .

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

Multiply ${(- 1)}^{0}$ by $- 1$ .

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

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

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

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

Add $0$ and $1$ .

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

Step 10

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

$- \frac{1}{1}$

Step 11

Cancel the common factor of $1$ .

Cancel the common factor.

$- \frac{1}{1}$

Rewrite the expression.

$- 1 \cdot 1$

Step 12

Multiply $- 1$ by $1$ .

$- 1$

Simplify -(-5a^-2bc)^0

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