Solve (4b^5c^-2)^3

$$( 4 b ^ { 5 } c ^ { - 2 } ) ^ { 3 }$$

Evaluate

$$\frac{64b^{15}}{c^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4b^{5}c^{-2}\right)^{3}$$

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

$$4^{3}\left(b^{5}\right)^{3}\left(c^{-2}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(b^{5}\right)^{3}\left(c^{-2}\right)^{3}$$

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

$$64b^{5\times 3}c^{-2\times 3}$$

Multiply 5 times 3.

$$64b^{15}c^{-2\times 3}$$

Multiply -2 times 3.

$$64b^{15}\times \frac{1}{c^{6}}$$

Expand

$$\frac{64b^{15}}{c^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4b^{5}c^{-2}\right)^{3}$$

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

$$4^{3}\left(b^{5}\right)^{3}\left(c^{-2}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(b^{5}\right)^{3}\left(c^{-2}\right)^{3}$$

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

$$64b^{5\times 3}c^{-2\times 3}$$

Multiply 5 times 3.

$$64b^{15}c^{-2\times 3}$$

Multiply -2 times 3.

$$64b^{15}\times \frac{1}{c^{6}}$$