Basic Math Examples

${(\frac{3}{4})}^{20} {(\frac{3}{4})}^{19} \div (- \frac{3}{4^{37}})$

Step 1

To divide by a fraction, multiply by its reciprocal.

${(\frac{3}{4})}^{20} {(\frac{3}{4})}^{19} (- \frac{4^{37}}{3})$

Step 2

Multiply ${(\frac{3}{4})}^{20}$ by ${(\frac{3}{4})}^{19}$ by adding the exponents.

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Step 2.1

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

${(\frac{3}{4})}^{20 + 19} (- \frac{4^{37}}{3})$

Step 2.2

Add $20$ and $19$ .

${(\frac{3}{4})}^{39} (- \frac{4^{37}}{3})$

Step 3

Apply the product rule to $\frac{3}{4}$ .

$\frac{3^{39}}{4^{39}} (- \frac{4^{37}}{3})$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Move the leading negative in $- \frac{4^{37}}{3}$ into the numerator.

$\frac{3^{39}}{4^{39}} \cdot \frac{- 4^{37}}{3}$

Step 4.2

Factor $3$ out of $3^{39}$ .

$\frac{3 \cdot 3^{38}}{4^{39}} \cdot \frac{- 4^{37}}{3}$

Step 4.3

Cancel the common factor.

$\frac{3 \cdot 3^{38}}{4^{39}} \cdot \frac{- 4^{37}}{3}$

Step 4.4

Rewrite the expression.

$\frac{3^{38}}{4^{39}} (- 4^{37})$

Step 5

Cancel the common factor of $4^{37}$ .

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Step 5.1

Factor $4^{37}$ out of $4^{39}$ .

$\frac{3^{38}}{4^{37} \cdot 4^{2}} (- 4^{37})$

Step 5.2

Factor $4^{37}$ out of $- 4^{37}$ .

$\frac{3^{38}}{4^{37} \cdot 4^{2}} (4^{37} \cdot - 1)$

Step 5.3

Cancel the common factor.

$\frac{3^{38}}{4^{37} \cdot 4^{2}} (4^{37} \cdot - 1)$

Step 5.4

Rewrite the expression.

$\frac{3^{38}}{4^{2}} \cdot - 1$

Step 6

Combine $\frac{3^{38}}{4^{2}}$ and $- 1$ .

$\frac{3^{38} \cdot - 1}{4^{2}}$

Step 7

Simplify the expression.

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Step 7.1

Raise $3$ to the power of $38$ .

$\frac{1350851717672990000 \cdot - 1}{4^{2}}$

Step 7.2

Raise $4$ to the power of $2$ .

$\frac{1350851717672990000 \cdot - 1}{16}$

Step 7.3

Multiply $1350851717672990000$ by $- 1$ .

$\frac{- 1350851717672990000}{16}$

Step 7.4

Divide $- 1350851717672990000$ by $16$ .

$- 84428232354561875$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 84428232354561875$

Decimal Form:

$- 8.44282323 \cdot 10^{16}$