Basic Math Examples

${(\frac{3}{8})}^{- 2} - {(\frac{3}{10})}^{- 2}$

Step 1

Simplify each term.

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Step 1.1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{8}{3})}^{2} - {(\frac{3}{10})}^{- 2}$

Step 1.2

Apply the product rule to $\frac{8}{3}$ .

$\frac{8^{2}}{3^{2}} - {(\frac{3}{10})}^{- 2}$

Step 1.3

Raise $8$ to the power of $2$ .

$\frac{64}{3^{2}} - {(\frac{3}{10})}^{- 2}$

Step 1.4

Raise $3$ to the power of $2$ .

$\frac{64}{9} - {(\frac{3}{10})}^{- 2}$

Step 1.5

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{64}{9} - {(\frac{10}{3})}^{2}$

Step 1.6

Apply the product rule to $\frac{10}{3}$ .

$\frac{64}{9} - \frac{10^{2}}{3^{2}}$

Step 1.7

Raise $10$ to the power of $2$ .

$\frac{64}{9} - \frac{100}{3^{2}}$

Step 1.8

Raise $3$ to the power of $2$ .

$\frac{64}{9} - \frac{100}{9}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{64 - 100}{9}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $100$ from $64$ .

$\frac{- 36}{9}$

Step 2.2.2

Divide $- 36$ by $9$ .

$- 4$