Algebra Examples

${(4^{- 3} \cdot 2^{- 3})}^{0}$

Step 1

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

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

Step 2

Raise $4$ to the power of $3$ .

${(\frac{1}{64} \cdot 2^{- 3})}^{0}$

Step 3

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

${(\frac{1}{64} \cdot \frac{1}{2^{3}})}^{0}$

Step 4

Combine fractions.

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Step 4.1

Combine.

${(\frac{1 \cdot 1}{64 \cdot 2^{3}})}^{0}$

Step 4.2

Multiply $1$ by $1$ .

${(\frac{1}{64 \cdot 2^{3}})}^{0}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $64$ as $2^{6}$ .

${(\frac{1}{2^{6} \cdot 2^{3}})}^{0}$

Step 5.2

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

${(\frac{1}{2^{6 + 3}})}^{0}$

Step 5.3

Add $6$ and $3$ .

${(\frac{1}{2^{9}})}^{0}$

Step 6

Simplify the expression.

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Step 6.1

Raise $2$ to the power of $9$ .

${(\frac{1}{512})}^{0}$

Step 6.2

Apply the product rule to $\frac{1}{512}$ .

$\frac{1^{0}}{512^{0}}$

Step 6.3

Anything raised to $0$ is $1$ .

$\frac{1}{512^{0}}$

Step 6.4

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 6.5

Divide $1$ by $1$ .

$1$