Evaluate (10q^5w^7)/(2w^3)*(4(q^6)^2)/(w^-5)

$\frac{10 q^{5} w^{7}}{2 w^{3}} \cdot \frac{4 {(q^{6})}^{2}}{w^{- 5}}$

Step 1

Combine.

$\frac{10 q^{5} w^{7} (4 {(q^{6})}^{2})}{2 w^{3} w^{- 5}}$

Step 2

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

Move $w^{- 5}$ .

$\frac{10 q^{5} w^{7} (4 {(q^{6})}^{2})}{2 (w^{- 5} w^{3})}$

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

$\frac{10 q^{5} w^{7} (4 {(q^{6})}^{2})}{2 w^{- 5 + 3}}$

Add $- 5$ and $3$ .

$\frac{10 q^{5} w^{7} (4 {(q^{6})}^{2})}{2 w^{- 2}}$

Step 3

Move $w^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{10 q^{5} w^{7} (4 {(q^{6})}^{2}) w^{2}}{2}$

Step 4

Multiply $w^{7}$ by $w^{2}$ by adding the exponents.

Move $w^{2}$ .

$\frac{10 q^{5} (w^{2} w^{7}) (4 {(q^{6})}^{2})}{2}$

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

$\frac{10 q^{5} w^{2 + 7} (4 {(q^{6})}^{2})}{2}$

Add $2$ and $7$ .

$\frac{10 q^{5} w^{9} (4 {(q^{6})}^{2})}{2}$

Step 5

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 q^{5} w^{9} (4 {(q^{6})}^{2})$ .

$\frac{2 (5 q^{5} w^{9} (4 {(q^{6})}^{2}))}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (5 q^{5} w^{9} (4 {(q^{6})}^{2}))}{2 (1)}$

Cancel the common factor.

$\frac{2 (5 q^{5} w^{9} (4 {(q^{6})}^{2}))}{2 \cdot 1}$

Rewrite the expression.

$\frac{5 q^{5} w^{9} (4 {(q^{6})}^{2})}{1}$

Divide $5 q^{5} w^{9} (4 {(q^{6})}^{2})$ by $1$ .

$5 q^{5} w^{9} (4 {(q^{6})}^{2})$

Step 6

Multiply the exponents in ${(q^{6})}^{2}$ .

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

$5 q^{5} w^{9} (4 q^{6 \cdot 2})$

Multiply $6$ by $2$ .

$5 q^{5} w^{9} (4 q^{12})$

Step 7

Multiply $q^{5}$ by $q^{12}$ by adding the exponents.

Move $q^{12}$ .

$5 (q^{12} q^{5}) w^{9} \cdot 4$

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

$5 q^{12 + 5} w^{9} \cdot 4$

Add $12$ and $5$ .

$5 q^{17} w^{9} \cdot 4$

Step 8

Multiply $4$ by $5$ .

$20 q^{17} w^{9}$

Evaluate (10q^5w^7)/(2w^3)*(4(q^6)^2)/(w^-5)

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