Solve (9/12a^-3b^5)^2

$$( \frac { 9 } { 12 } a ^ { - 3 } b ^ { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{9b^{10}}{16a^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise \frac{3}{4} to the power 2.

$$\frac{9}{16}\left(a^{-3}\right)^{2}\left(b^{5}\right)^{2}$$

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

$$\frac{9}{16}a^{-3\times 2}b^{5\times 2}$$

Multiply -3 times 2.

$$\frac{9}{16}\times \frac{1}{a^{6}}b^{5\times 2}$$

Multiply 5 times 2.

$$\frac{9}{16}\times \frac{1}{a^{6}}b^{10}$$

Expand

$$\frac{9b^{10}}{16a^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise \frac{3}{4} to the power 2.

$$\frac{9}{16}\left(a^{-3}\right)^{2}\left(b^{5}\right)^{2}$$

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

$$\frac{9}{16}a^{-3\times 2}b^{5\times 2}$$

Multiply -3 times 2.

$$\frac{9}{16}\times \frac{1}{a^{6}}b^{5\times 2}$$

Multiply 5 times 2.

$$\frac{9}{16}\times \frac{1}{a^{6}}b^{10}$$