Solve (4x^4y^-7)^3

$$( 4 x ^ { 4 } y ^ { - 7 } ) ^ { 3 }$$

Evaluate

$$\frac{64x^{12}}{y^{21}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4x^{4}y^{-7}\right)^{3}$$

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

$$4^{3}\left(x^{4}\right)^{3}\left(y^{-7}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(x^{4}\right)^{3}\left(y^{-7}\right)^{3}$$

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

$$64x^{4\times 3}y^{-7\times 3}$$

Multiply 4 times 3.

$$64x^{12}y^{-7\times 3}$$

Multiply -7 times 3.

$$64x^{12}\times \frac{1}{y^{21}}$$

Expand

$$\frac{64x^{12}}{y^{21}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4x^{4}y^{-7}\right)^{3}$$

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

$$4^{3}\left(x^{4}\right)^{3}\left(y^{-7}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(x^{4}\right)^{3}\left(y^{-7}\right)^{3}$$

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

$$64x^{4\times 3}y^{-7\times 3}$$

Multiply 4 times 3.

$$64x^{12}y^{-7\times 3}$$

Multiply -7 times 3.

$$64x^{12}\times \frac{1}{y^{21}}$$