Algebra Examples

${(2 d)}^{0} \div {(d^{2} e^{- 4})}^{- 1}$

Step 1

Rewrite the division as a fraction.

$\frac{{(2 d)}^{0}}{{(d^{2} e^{- 4})}^{- 1}}$

Step 2

Move ${(d^{2} e^{- 4})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(2 d)}^{0} (d^{2} e^{- 4})$

Step 3

Rewrite using the commutative property of multiplication.

$e^{- 4} {(2 d)}^{0} d^{2}$

Step 4

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

$\frac{1}{e^{4}} {(2 d)}^{0} d^{2}$

Step 5

Apply the product rule to $2 d$ .

$\frac{1}{e^{4}} (2^{0} d^{0}) d^{2}$

Step 6

Multiply $d^{0}$ by $d^{2}$ by adding the exponents.

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Step 6.1

Move $d^{2}$ .

$\frac{1}{e^{4}} (2^{0} (d^{2} d^{0}))$

Step 6.2

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

$\frac{1}{e^{4}} (2^{0} d^{2 + 0})$

Step 6.3

Add $2$ and $0$ .

$\frac{1}{e^{4}} (2^{0} d^{2})$

Step 7

Simplify $\frac{1}{e^{4}} (2^{0} d^{2})$ .

$\frac{1}{e^{4}} d^{2}$

Step 8

Combine $\frac{1}{e^{4}}$ and $d^{2}$ .

$\frac{d^{2}}{e^{4}}$