Pre-Algebra Examples

${(2 m^{3})}^{0} {(3 m^{6})}^{- 1}$

Step 1

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

$2^{0} {(m^{3})}^{0} {(3 m^{6})}^{- 1}$

Step 2

Anything raised to $0$ is $1$ .

$1 {(m^{3})}^{0} {(3 m^{6})}^{- 1}$

Step 3

Multiply ${(m^{3})}^{0}$ by $1$ .

${(m^{3})}^{0} {(3 m^{6})}^{- 1}$

Step 4

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

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Step 4.1

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

$m^{3 \cdot 0} {(3 m^{6})}^{- 1}$

Step 4.2

Multiply $3$ by $0$ .

$m^{0} {(3 m^{6})}^{- 1}$

Step 5

Anything raised to $0$ is $1$ .

$1 {(3 m^{6})}^{- 1}$

Step 6

Multiply ${(3 m^{6})}^{- 1}$ by $1$ .

${(3 m^{6})}^{- 1}$

Step 7

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

$\frac{1}{3 m^{6}}$