Simplify (8c^(7/2)(3k^(3/8)))(3k^(7/2)(8c^(3/8)))

$(8 c^{\frac{7}{2}} \cdot (3 k^{\frac{3}{8}})) (3 k^{\frac{7}{2}} \cdot (8 c^{\frac{3}{8}}))$

Step 1

Multiply $c^{\frac{7}{2}}$ by $c^{\frac{3}{8}}$ by adding the exponents.

Move $c^{\frac{3}{8}}$ .

$8 (c^{\frac{3}{8}} c^{\frac{7}{2}}) \cdot (3 k^{\frac{3}{8}}) (3 k^{\frac{7}{2}} \cdot (8))$

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

$8 c^{\frac{3}{8} + \frac{7}{2}} \cdot (3 k^{\frac{3}{8}}) (3 k^{\frac{7}{2}} \cdot (8))$

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$8 c^{\frac{3}{8} + \frac{7}{2} \cdot \frac{4}{4}} \cdot (3 k^{\frac{3}{8}}) (3 k^{\frac{7}{2}} \cdot (8))$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{2}$ by $\frac{4}{4}$ .

$8 c^{\frac{3}{8} + \frac{7 \cdot 4}{2 \cdot 4}} \cdot (3 k^{\frac{3}{8}}) (3 k^{\frac{7}{2}} \cdot (8))$

Multiply $2$ by $4$ .

$8 c^{\frac{3}{8} + \frac{7 \cdot 4}{8}} \cdot (3 k^{\frac{3}{8}}) (3 k^{\frac{7}{2}} \cdot (8))$

Combine the numerators over the common denominator.

$8 c^{\frac{3 + 7 \cdot 4}{8}} \cdot (3 k^{\frac{3}{8}}) (3 k^{\frac{7}{2}} \cdot (8))$

Simplify the numerator.

Multiply $7$ by $4$ .

$8 c^{\frac{3 + 28}{8}} \cdot (3 k^{\frac{3}{8}}) (3 k^{\frac{7}{2}} \cdot (8))$

Add $3$ and $28$ .

$8 c^{\frac{31}{8}} \cdot (3 k^{\frac{3}{8}}) (3 k^{\frac{7}{2}} \cdot (8))$

Step 2

Multiply $k^{\frac{3}{8}}$ by $k^{\frac{7}{2}}$ by adding the exponents.

Move $k^{\frac{7}{2}}$ .

$8 c^{\frac{31}{8}} \cdot (3 (k^{\frac{7}{2}} k^{\frac{3}{8}})) (3 \cdot (8))$

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

$8 c^{\frac{31}{8}} \cdot (3 k^{\frac{7}{2} + \frac{3}{8}}) (3 \cdot (8))$

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$8 c^{\frac{31}{8}} \cdot (3 k^{\frac{7}{2} \cdot \frac{4}{4} + \frac{3}{8}}) (3 \cdot (8))$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{2}$ by $\frac{4}{4}$ .

$8 c^{\frac{31}{8}} \cdot (3 k^{\frac{7 \cdot 4}{2 \cdot 4} + \frac{3}{8}}) (3 \cdot (8))$

Multiply $2$ by $4$ .

$8 c^{\frac{31}{8}} \cdot (3 k^{\frac{7 \cdot 4}{8} + \frac{3}{8}}) (3 \cdot (8))$

Combine the numerators over the common denominator.

$8 c^{\frac{31}{8}} \cdot (3 k^{\frac{7 \cdot 4 + 3}{8}}) (3 \cdot (8))$

Simplify the numerator.

Multiply $7$ by $4$ .

$8 c^{\frac{31}{8}} \cdot (3 k^{\frac{28 + 3}{8}}) (3 \cdot (8))$

Add $28$ and $3$ .

$8 c^{\frac{31}{8}} \cdot (3 k^{\frac{31}{8}}) (3 \cdot (8))$

Step 3

Rewrite using the commutative property of multiplication.

$8 \cdot 3 c^{\frac{31}{8}} k^{\frac{31}{8}} (3 \cdot (8))$

Step 4

Multiply $8$ by $3$ .

$24 c^{\frac{31}{8}} k^{\frac{31}{8}} (3 \cdot (8))$

Step 5

Multiply $3$ by $8$ .

$24 c^{\frac{31}{8}} k^{\frac{31}{8}} \cdot 24$

Step 6

Multiply $24$ by $24$ .

$576 c^{\frac{31}{8}} k^{\frac{31}{8}}$

Simplify (8c^(7/2)*(3k^(3/8)))(3k^(7/2)*(8c^(3/8)))

Related Questions

Simplify (8c^(7/2)(3k^(3/8)))(3k^(7/2)(8c^(3/8)))