Simplify (3/5d^3)(5/3d^5)

$(\frac{3}{5} d^{3}) (\frac{5}{3} d^{5})$

Step 1

Rewrite using the commutative property of multiplication.

$\frac{3}{5} \cdot \frac{5}{3} d^{3} d^{5}$

Step 2

Multiply $d^{3}$ by $d^{5}$ by adding the exponents.

Move $d^{5}$ .

$\frac{3}{5} \cdot \frac{5}{3} (d^{5} d^{3})$

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

$\frac{3}{5} \cdot \frac{5}{3} d^{5 + 3}$

Add $5$ and $3$ .

$\frac{3}{5} \cdot \frac{5}{3} d^{8}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5}{3} d^{8}$

Rewrite the expression.

$\frac{1}{5} \cdot 5 d^{8}$

Step 4

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{5} \cdot 5 d^{8}$

Rewrite the expression.

$1 d^{8}$

Step 5

Multiply $d^{8}$ by $1$ .

$d^{8}$