Solve 1/25a^{3}b^{2}*(-5a^{2}b^{3})-1/10a^{2}b^{3}*(-2a^3b^2)+18a^5-1/2a*(36a^4)=

$$\frac { 1 } { 25 } a ^ { 3 } b ^ { 2 } \cdot ( - 5 a ^ { 2 } b ^ { 3 } ) - \frac { 1 } { 10 } a ^ { 2 } b ^ { 3 } \cdot ( - 2 a ^ { 3 } b ^ { 2 } ) + 18 a ^ { 5 } - \frac { 1 } { 2 } a \cdot ( 36 a ^ { 4 } ) =$$

Evaluate

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Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{1}{25}a^{5}b^{2}\left(-5\right)b^{3}-\frac{1}{10}a^{2}b^{3}\left(-2\right)a^{3}b^{2}+18a^{5}-\frac{1}{2}a\times 36a^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{1}{25}a^{5}b^{5}\left(-5\right)-\frac{1}{10}a^{2}b^{3}\left(-2\right)a^{3}b^{2}+18a^{5}-\frac{1}{2}a\times 36a^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{1}{25}a^{5}b^{5}\left(-5\right)-\frac{1}{10}a^{5}b^{3}\left(-2\right)b^{2}+18a^{5}-\frac{1}{2}a\times 36a^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{1}{25}a^{5}b^{5}\left(-5\right)-\frac{1}{10}a^{5}b^{5}\left(-2\right)+18a^{5}-\frac{1}{2}a\times 36a^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{1}{25}a^{5}b^{5}\left(-5\right)-\frac{1}{10}a^{5}b^{5}\left(-2\right)+18a^{5}-\frac{1}{2}a^{5}\times 36$$

Multiply \frac{1}{25} and -5 to get -\frac{1}{5}.

$$-\frac{1}{5}a^{5}b^{5}-\frac{1}{10}a^{5}b^{5}\left(-2\right)+18a^{5}-\frac{1}{2}a^{5}\times 36$$

Multiply \frac{1}{10} and -2 to get -\frac{1}{5}.

$$-\frac{1}{5}a^{5}b^{5}-\left(-\frac{1}{5}a^{5}b^{5}\right)+18a^{5}-\frac{1}{2}a^{5}\times 36$$

The opposite of -\frac{1}{5}a^{5}b^{5} is \frac{1}{5}a^{5}b^{5}.

$$-\frac{1}{5}a^{5}b^{5}+\frac{1}{5}a^{5}b^{5}+18a^{5}-\frac{1}{2}a^{5}\times 36$$

Combine -\frac{1}{5}a^{5}b^{5} and \frac{1}{5}a^{5}b^{5} to get 0.

$$0+18a^{5}-\frac{1}{2}a^{5}\times 36$$

Anything plus zero gives itself.

$$18a^{5}-\frac{1}{2}a^{5}\times 36$$

Multiply \frac{1}{2} and 36 to get 18.

$$18a^{5}-18a^{5}$$

Combine 18a^{5} and -18a^{5} to get 0.

$$0$$

Factor

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Solution Steps

Factor out \frac{1}{5}.

$$\frac{-a^{3}b^{2}a^{2}b^{3}+a^{2}b^{3}a^{3}b^{2}+90a^{5}-90aa^{4}}{5}$$

Consider -a^{5}b^{5}+a^{5}b^{5}+90a^{5}-90a^{5}. Factor out a^{5}.

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