Solve (a^3/m)^-4

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

Evaluate

$$\frac{m^{4}}{a^{12}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{3}}{m^{1}}\right)^{-4}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{\left(a^{3}\right)^{-4}}{\left(m^{1}\right)^{-4}}$$

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

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

Multiply 3 times -4.

$$\frac{a^{-12}}{m^{-4}}$$

Multiply 1 times -4.

$$\frac{1}{a^{12}m^{-4}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(a^{3}\times \frac{1}{m}\right)^{-4}$$

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

$$\left(a^{3}\right)^{-4}\times \left(\frac{1}{m}\right)^{-4}$$

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

$$a^{3\left(-4\right)}m^{-\left(-4\right)}$$

Multiply 3 times -4.

$$\frac{1}{a^{12}}m^{-\left(-4\right)}$$

Multiply -1 times -4.

$$\frac{1}{a^{12}}m^{4}$$

Expand

$$\frac{m^{4}}{a^{12}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{3}}{m^{1}}\right)^{-4}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{\left(a^{3}\right)^{-4}}{\left(m^{1}\right)^{-4}}$$

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

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

Multiply 3 times -4.

$$\frac{a^{-12}}{m^{-4}}$$

Multiply 1 times -4.

$$\frac{1}{a^{12}m^{-4}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(a^{3}\times \frac{1}{m}\right)^{-4}$$

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

$$\left(a^{3}\right)^{-4}\times \left(\frac{1}{m}\right)^{-4}$$

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

$$a^{3\left(-4\right)}m^{-\left(-4\right)}$$

Multiply 3 times -4.

$$\frac{1}{a^{12}}m^{-\left(-4\right)}$$

Multiply -1 times -4.

$$\frac{1}{a^{12}}m^{4}$$