Simplify (1/3)^6(-12(1/3)^9)(1/3)^4

${(\frac{1}{3})}^{6} (- 12 {(\frac{1}{3})}^{9}) {(\frac{1}{3})}^{4}$

Step 1

Multiply ${(\frac{1}{3})}^{6}$ by ${(\frac{1}{3})}^{9}$ by adding the exponents.

Move ${(\frac{1}{3})}^{9}$ .

${(\frac{1}{3})}^{9} {(\frac{1}{3})}^{6} \cdot - 12 {(\frac{1}{3})}^{4}$

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

${(\frac{1}{3})}^{9 + 6} \cdot - 12 {(\frac{1}{3})}^{4}$

Add $9$ and $6$ .

${(\frac{1}{3})}^{15} \cdot - 12 {(\frac{1}{3})}^{4}$

Step 2

Multiply ${(\frac{1}{3})}^{15}$ by ${(\frac{1}{3})}^{4}$ by adding the exponents.

Move ${(\frac{1}{3})}^{4}$ .

${(\frac{1}{3})}^{4} {(\frac{1}{3})}^{15} \cdot - 12$

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

${(\frac{1}{3})}^{4 + 15} \cdot - 12$

Add $4$ and $15$ .

${(\frac{1}{3})}^{19} \cdot - 12$

Step 3

Simplify the expression.

Apply the product rule to $\frac{1}{3}$ .

$\frac{1^{19}}{3^{19}} \cdot - 12$

One to any power is one.

$\frac{1}{3^{19}} \cdot - 12$

Raise $3$ to the power of $19$ .

$\frac{1}{1162261467} \cdot - 12$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $1162261467$ .

$\frac{1}{3 (387420489)} \cdot - 12$

Factor $3$ out of $- 12$ .

$\frac{1}{3 \cdot 387420489} \cdot (3 \cdot - 4)$

Cancel the common factor.

$\frac{1}{3 \cdot 387420489} \cdot (3 \cdot - 4)$

Rewrite the expression.

$\frac{1}{387420489} \cdot - 4$

Step 5

Combine $\frac{1}{387420489}$ and $- 4$ .

$\frac{- 4}{387420489}$

Step 6

Move the negative in front of the fraction.

$- \frac{4}{387420489}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{387420489}$

Decimal Form:

$- 1.03246991 \cdot 10^{- 8}$

Simplify (1/3)^6(-12(1/3)^9)(1/3)^4

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