Simplify (3d^-10)÷6d^-7

$3 d^{- 10} \div 6 d^{- 7}$

Step 1

Rewrite the division as a fraction.

$\frac{3 d^{- 10}}{6 d^{- 7}}$

Step 2

Move $d^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3}{6 d^{- 7} d^{10}}$

Step 3

Multiply $d^{- 7}$ by $d^{10}$ by adding the exponents.

Move $d^{10}$ .

$\frac{3}{6 (d^{10} d^{- 7})}$

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

$\frac{3}{6 d^{10 - 7}}$

Subtract $7$ from $10$ .

$\frac{3}{6 d^{3}}$

Step 4

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$\frac{3 (1)}{6 d^{3}}$

Cancel the common factors.

Factor $3$ out of $6 d^{3}$ .

$\frac{3 (1)}{3 (2 d^{3})}$

Cancel the common factor.

$\frac{3 \cdot 1}{3 (2 d^{3})}$

Rewrite the expression.

$\frac{1}{2 d^{3}}$