Solve (3,375f^9g^-21)^-1/3

$$( 3,375 f ^ { 9 } g ^ { - 21 } ) ^ { - 1 / 3 }$$

Evaluate

$$\frac{g^{7}}{15f^{3}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3375f^{9}g^{-21}\right)^{-\frac{1}{3}}$$

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

$$3375^{-\frac{1}{3}}\left(f^{9}\right)^{-\frac{1}{3}}\left(g^{-21}\right)^{-\frac{1}{3}}$$

Raise 3375 to the power -\frac{1}{3}.

$$\frac{1}{15}\left(f^{9}\right)^{-\frac{1}{3}}\left(g^{-21}\right)^{-\frac{1}{3}}$$

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

$$\frac{1}{15}f^{9\left(-\frac{1}{3}\right)}g^{-21\left(-\frac{1}{3}\right)}$$

Multiply 9 times -\frac{1}{3}.

$$\frac{1}{15}\times \frac{1}{f^{3}}g^{-21\left(-\frac{1}{3}\right)}$$

Multiply -21 times -\frac{1}{3}.

$$\frac{1}{15}\times \frac{1}{f^{3}}g^{7}$$

Differentiate w.r.t. f

$$-\frac{g^{7}}{5f^{4}}$$