Write in Standard Form (-6a^4b^3)^2*-2ab^5

${(- 6 a^{4} b^{3})}^{2} \cdot - 2 a b^{5}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- 6 a^{4} b^{3}$ .

${(- 6 a^{4})}^{2} {(b^{3})}^{2} \cdot - 2 a b^{5}$

Apply the product rule to $- 6 a^{4}$ .

${(- 6)}^{2} {(a^{4})}^{2} {(b^{3})}^{2} \cdot - 2 a b^{5}$

Step 3

Raise $- 6$ to the power of $2$ .

$36 {(a^{4})}^{2} {(b^{3})}^{2} \cdot - 2 a b^{5}$

Step 4

Multiply the exponents in ${(a^{4})}^{2}$ .

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

$36 a^{4 \cdot 2} {(b^{3})}^{2} \cdot - 2 a b^{5}$

Multiply $4$ by $2$ .

$36 a^{8} {(b^{3})}^{2} \cdot - 2 a b^{5}$

Step 5

Multiply $a^{8}$ by $a$ by adding the exponents.

Move $a$ .

$36 (a \cdot a^{8}) {(b^{3})}^{2} \cdot - 2 b^{5}$

Multiply $a$ by $a^{8}$ .

Raise $a$ to the power of $1$ .

$36 (a^{1} a^{8}) {(b^{3})}^{2} \cdot - 2 b^{5}$

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

$36 a^{1 + 8} {(b^{3})}^{2} \cdot - 2 b^{5}$

Add $1$ and $8$ .

$36 a^{9} {(b^{3})}^{2} \cdot - 2 b^{5}$

Step 6

Multiply the exponents in ${(b^{3})}^{2}$ .

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

$36 a^{9} b^{3 \cdot 2} \cdot - 2 b^{5}$

Multiply $3$ by $2$ .

$36 a^{9} b^{6} \cdot - 2 b^{5}$

Step 7

Multiply $b^{6}$ by $b^{5}$ by adding the exponents.

Move $b^{5}$ .

$36 a^{9} (b^{5} b^{6}) \cdot - 2$

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

$36 a^{9} b^{5 + 6} \cdot - 2$

Add $5$ and $6$ .

$36 a^{9} b^{11} \cdot - 2$

Step 8

Multiply $- 2$ by $36$ .

$- 72 a^{9} b^{11}$

Write in Standard Form (-6a^4b^3)^2*-2ab^5

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