Simplify ((3d^-2)^-4)/(3d^10q)

$\frac{{(3 d^{- 2})}^{- 4}}{3 d^{10} q}$

Step 1

Move ${(3 d^{- 2})}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3 d^{10} q {(3 d^{- 2})}^{4}}$

Step 2

Simplify the denominator.

Apply the product rule to $3 d^{- 2}$ .

$\frac{1}{3 d^{10} q \cdot 3^{4} {(d^{- 2})}^{4}}$

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

Move $3^{4}$ .

$\frac{1}{3^{4} \cdot 3 d^{10} q {(d^{- 2})}^{4}}$

Multiply $3^{4}$ by $3$ .

Raise $3$ to the power of $1$ .

$\frac{1}{3^{4} \cdot 3^{1} d^{10} q {(d^{- 2})}^{4}}$

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

$\frac{1}{3^{4 + 1} d^{10} q {(d^{- 2})}^{4}}$

Add $4$ and $1$ .

$\frac{1}{3^{5} d^{10} q {(d^{- 2})}^{4}}$

Raise $3$ to the power of $5$ .

$\frac{1}{243 d^{10} q {(d^{- 2})}^{4}}$

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

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

$\frac{1}{243 d^{10} q d^{- 2 \cdot 4}}$

Multiply $- 2$ by $4$ .

$\frac{1}{243 d^{10} q d^{- 8}}$

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

$\frac{1}{243 d^{10} q \frac{1}{d^{8}}}$

Combine exponents.

Combine $243$ and $\frac{1}{d^{8}}$ .

$\frac{1}{d^{10} q \frac{243}{d^{8}}}$

Combine $d^{10}$ and $\frac{243}{d^{8}}$ .

$\frac{1}{q \frac{d^{10} \cdot 243}{d^{8}}}$

Combine $q$ and $\frac{d^{10} \cdot 243}{d^{8}}$ .

$\frac{1}{\frac{q (d^{10} \cdot 243)}{d^{8}}}$

Remove unnecessary parentheses.

$\frac{1}{\frac{q d^{10} \cdot 243}{d^{8}}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{q d^{10} \cdot 243}{d^{8}}$ by cancelling the common factors.

Factor $d^{8}$ out of $q d^{10} \cdot 243$ .

$\frac{1}{\frac{d^{8} (q d^{2} \cdot 243)}{d^{8}}}$

Multiply by $1$ .

$\frac{1}{\frac{d^{8} (q d^{2} \cdot 243)}{d^{8} \cdot 1}}$

Cancel the common factor.

$\frac{1}{\frac{d^{8} (q d^{2} \cdot 243)}{d^{8} \cdot 1}}$

Rewrite the expression.

$\frac{1}{\frac{q d^{2} \cdot 243}{1}}$

Divide $q d^{2} \cdot 243$ by $1$ .

$\frac{1}{q d^{2} \cdot 243}$

Step 3

Move $243$ to the left of $q d^{2}$ .

$\frac{1}{243 q d^{2}}$

Simplify ((3d^-2)^-4)/(3d^10q)

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