Simplify 9d^-5*((36d^6)÷4d^2)

$9 d^{- 5} \cdot (36 d^{6} \div 4 d^{2})$

Step 1

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

$9 \frac{1}{d^{5}} \cdot 36 d^{6} \div 4 d^{2}$

Step 2

Combine $9$ and $\frac{1}{d^{5}}$ .

$\frac{9}{d^{5}} \cdot 36 d^{6} \div 4 d^{2}$

Step 3

Combine.

$\frac{9 (36 d^{6})}{d^{5} (4 d^{2})}$

Step 4

Multiply $d^{5}$ by $d^{2}$ by adding the exponents.

Move $d^{2}$ .

$\frac{9 (36 d^{6})}{d^{2} d^{5} \cdot 4}$

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

$\frac{9 (36 d^{6})}{d^{2 + 5} \cdot 4}$

Add $2$ and $5$ .

$\frac{9 (36 d^{6})}{d^{7} \cdot 4}$

Step 5

Reduce the expression by cancelling the common factors.

Cancel the common factor of $36$ and $4$ .

Factor $4$ out of $9 (36 d^{6})$ .

$\frac{4 (9 (9 d^{6}))}{d^{7} \cdot 4}$

Cancel the common factors.

Factor $4$ out of $d^{7} \cdot 4$ .

$\frac{4 (9 (9 d^{6}))}{4 \cdot d^{7}}$

Cancel the common factor.

$\frac{4 (9 (9 d^{6}))}{4 \cdot d^{7}}$

Rewrite the expression.

$\frac{9 (9 d^{6})}{d^{7}}$

Cancel the common factor of $d^{6}$ and $d^{7}$ .

Factor $d^{6}$ out of $9 (9 d^{6})$ .

$\frac{d^{6} (9 \cdot (9))}{d^{7}}$

Cancel the common factors.

Factor $d^{6}$ out of $d^{7}$ .

$\frac{d^{6} (9 \cdot (9))}{d^{6} d}$

Cancel the common factor.

$\frac{d^{6} (9 \cdot (9))}{d^{6} d}$

Rewrite the expression.

$\frac{9 \cdot (9)}{d}$

Step 6

Multiply $9$ by $9$ .

$\frac{81}{d}$