Solve (-5a^2b)^2div5a^3b^2

$$( - 5 a ^ { 2 } b ) ^ { 2 } \div 5 a ^ { 3 } b ^ { 2 }$$

Evaluate

$$5b^{4}a^{7}$$

Solution Steps

Expand \left(-5a^{2}b\right)^{2}.

$$\frac{\left(-5\right)^{2}\left(a^{2}\right)^{2}b^{2}}{5}a^{3}b^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(-5\right)^{2}a^{4}b^{2}}{5}a^{3}b^{2}$$

Calculate -5 to the power of 2 and get 25.

$$\frac{25a^{4}b^{2}}{5}a^{3}b^{2}$$

Divide 25a^{4}b^{2} by 5 to get 5a^{4}b^{2}.

$$5a^{4}b^{2}a^{3}b^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$5a^{7}b^{2}b^{2}$$

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

$$5a^{7}b^{4}$$

Expand

$$5b^{4}a^{7}$$

Solution Steps

Expand \left(-5a^{2}b\right)^{2}.

$$\frac{\left(-5\right)^{2}\left(a^{2}\right)^{2}b^{2}}{5}a^{3}b^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(-5\right)^{2}a^{4}b^{2}}{5}a^{3}b^{2}$$

Calculate -5 to the power of 2 and get 25.

$$\frac{25a^{4}b^{2}}{5}a^{3}b^{2}$$

Divide 25a^{4}b^{2} by 5 to get 5a^{4}b^{2}.

$$5a^{4}b^{2}a^{3}b^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$5a^{7}b^{2}b^{2}$$

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

$$5a^{7}b^{4}$$