Solve (-4/7a^3b^2)^2

$$( - \frac { 4 } { 7 } a ^ { 3 } b ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{16b^{4}a^{6}}{49}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{4}{7}a^{3}b^{2}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-\frac{4}{7}\right)^{2}\left(a^{3}\right)^{2}\left(b^{2}\right)^{2}$$

Raise -\frac{4}{7} to the power 2.

$$\frac{16}{49}\left(a^{3}\right)^{2}\left(b^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$\frac{16}{49}a^{3\times 2}b^{2\times 2}$$

Multiply 3 times 2.

$$\frac{16}{49}a^{6}b^{2\times 2}$$

Multiply 2 times 2.

$$\frac{16}{49}a^{6}b^{4}$$

Expand

$$\frac{16b^{4}a^{6}}{49}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{4}{7}a^{3}b^{2}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-\frac{4}{7}\right)^{2}\left(a^{3}\right)^{2}\left(b^{2}\right)^{2}$$

Raise -\frac{4}{7} to the power 2.

$$\frac{16}{49}\left(a^{3}\right)^{2}\left(b^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$\frac{16}{49}a^{3\times 2}b^{2\times 2}$$

Multiply 3 times 2.

$$\frac{16}{49}a^{6}b^{2\times 2}$$

Multiply 2 times 2.

$$\frac{16}{49}a^{6}b^{4}$$