Solve (a^2/b)^24

$$( \frac { a ^ { 2 } } { b } ) ^ { 24 }$$

Evaluate

$$\frac{a^{48}}{b^{24}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{2}}{b^{1}}\right)^{24}$$

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

$$\frac{\left(a^{2}\right)^{24}}{\left(b^{1}\right)^{24}}$$

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

$$\frac{a^{2\times 24}}{b^{24}}$$

Multiply 2 times 24.

$$\frac{a^{48}}{b^{24}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(a^{2}\times \frac{1}{b}\right)^{24}$$

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

$$\left(a^{2}\right)^{24}\times \left(\frac{1}{b}\right)^{24}$$

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

$$a^{2\times 24}b^{-24}$$

Multiply 2 times 24.

$$a^{48}b^{-24}$$

Multiply -1 times 24.

$$a^{48}\times \frac{1}{b^{24}}$$

Expand

$$\frac{a^{48}}{b^{24}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{2}}{b^{1}}\right)^{24}$$

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

$$\frac{\left(a^{2}\right)^{24}}{\left(b^{1}\right)^{24}}$$

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

$$\frac{a^{2\times 24}}{b^{24}}$$

Multiply 2 times 24.

$$\frac{a^{48}}{b^{24}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(a^{2}\times \frac{1}{b}\right)^{24}$$

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

$$\left(a^{2}\right)^{24}\times \left(\frac{1}{b}\right)^{24}$$

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

$$a^{2\times 24}b^{-24}$$

Multiply 2 times 24.

$$a^{48}b^{-24}$$

Multiply -1 times 24.

$$a^{48}\times \frac{1}{b^{24}}$$