Finite Math Examples

$\frac{{(7 d^{- 2})}^{- 1}}{{(7 d)}^{- 2}}$

Step 1

Simplify the expression.

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Step 1.1

Move ${(7 d^{- 2})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(7 d)}^{- 2} (7 d^{- 2})}$

Step 1.2

Move ${(7 d)}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(7 d)}^{2}}{7 d^{- 2}}$

Step 1.3

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

$\frac{{(7 d)}^{2} d^{2}}{7}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $7 d$ .

$\frac{7^{2} d^{2} d^{2}}{7}$

Step 2.2

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

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Step 2.2.1

Move $d^{2}$ .

$\frac{7^{2} (d^{2} d^{2})}{7}$

Step 2.2.2

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

$\frac{7^{2} d^{2 + 2}}{7}$

Step 2.2.3

Add $2$ and $2$ .

$\frac{7^{2} d^{4}}{7}$

Step 2.3

Raise $7$ to the power of $2$ .

$\frac{49 d^{4}}{7}$

Step 3

Cancel the common factor of $49$ and $7$ .

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Step 3.1

Factor $7$ out of $49 d^{4}$ .

$\frac{7 (7 d^{4})}{7}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $7$ .

$\frac{7 (7 d^{4})}{7 (1)}$

Step 3.2.2

Cancel the common factor.

$\frac{7 (7 d^{4})}{7 \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{7 d^{4}}{1}$

Step 3.2.4

Divide $7 d^{4}$ by $1$ .

$7 d^{4}$