Solve frac{(-2a^{3}b)^{2}(5a^4b^6)}{-10a^3b^4}

$$\frac { ( - 2 a ^ { 3 } b ) ^ { 2 } ( 5 a ^ { 4 } b ^ { 6 } ) } { - 10 a ^ { 3 } b ^ { 4 } }$$

Evaluate

$$-2b^{4}a^{7}$$

Solution Steps

Cancel out 5a^{3}b^{4} in both numerator and denominator.

$$\frac{ab^{2}\left(-2ba^{3}\right)^{2}}{-2}$$

Expand \left(-2ba^{3}\right)^{2}.

$$\frac{ab^{2}\left(-2\right)^{2}b^{2}\left(a^{3}\right)^{2}}{-2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{ab^{2}\left(-2\right)^{2}b^{2}a^{6}}{-2}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{ab^{2}\times 4b^{2}a^{6}}{-2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{ab^{4}\times 4a^{6}}{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{a^{7}b^{4}\times 4}{-2}$$

Divide a^{7}b^{4}\times 4 by -2 to get a^{7}b^{4}\left(-2\right).

$$a^{7}b^{4}\left(-2\right)$$

Expand

$$-2b^{4}a^{7}$$

Solution Steps

Cancel out 5a^{3}b^{4} in both numerator and denominator.

$$\frac{ab^{2}\left(-2ba^{3}\right)^{2}}{-2}$$

Expand \left(-2ba^{3}\right)^{2}.

$$\frac{ab^{2}\left(-2\right)^{2}b^{2}\left(a^{3}\right)^{2}}{-2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{ab^{2}\left(-2\right)^{2}b^{2}a^{6}}{-2}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{ab^{2}\times 4b^{2}a^{6}}{-2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{ab^{4}\times 4a^{6}}{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{a^{7}b^{4}\times 4}{-2}$$

Divide a^{7}b^{4}\times 4 by -2 to get a^{7}b^{4}\left(-2\right).

$$a^{7}b^{4}\left(-2\right)$$