Solve (4/5a^-3b^4)^-3

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

Evaluate

$$\frac{125a^{9}}{64b^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise \frac{4}{5} to the power -3.

$$\frac{125}{64}\left(a^{-3}\right)^{-3}\left(b^{4}\right)^{-3}$$

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

$$\frac{125}{64}a^{-3\left(-3\right)}b^{4\left(-3\right)}$$

Multiply -3 times -3.

$$\frac{125}{64}a^{9}b^{4\left(-3\right)}$$

Multiply 4 times -3.

$$\frac{125}{64}a^{9}\times \frac{1}{b^{12}}$$

Expand

$$\frac{125a^{9}}{64b^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise \frac{4}{5} to the power -3.

$$\frac{125}{64}\left(a^{-3}\right)^{-3}\left(b^{4}\right)^{-3}$$

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

$$\frac{125}{64}a^{-3\left(-3\right)}b^{4\left(-3\right)}$$

Multiply -3 times -3.

$$\frac{125}{64}a^{9}b^{4\left(-3\right)}$$

Multiply 4 times -3.

$$\frac{125}{64}a^{9}\times \frac{1}{b^{12}}$$