Algebra Examples

${(3^{2} \times 3^{- 4})}^{4}$

Step 1

Multiply $3^{2}$ by $3^{- 4}$ by adding the exponents.

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Step 1.1

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

${(3^{2 - 4})}^{4}$

Step 1.2

Subtract $4$ from $2$ .

${(3^{- 2})}^{4}$

Step 2

Multiply the exponents in ${(3^{- 2})}^{4}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{- 2 \cdot 4}$

Step 2.2

Multiply $- 2$ by $4$ .

$3^{- 8}$

Step 3

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

$\frac{1}{3^{8}}$

Step 4

Raise $3$ to the power of $8$ .

$\frac{1}{6561}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6561}$

Decimal Form:

$0.00015241 \dots$