Solve (b^{-3}c^{-7})^-2(b^3c^-2)^-3

$$( b ^ { - 3 } c ^ { - 7 } ) ^ { - 2 } ( b ^ { 3 } c ^ { - 2 } ) ^ { - 3 }$$

Evaluate

$$\frac{c^{20}}{b^{3}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(b^{-3}c^{-7}\right)^{-2}\left(b^{3}c^{-2}\right)^{-3}$$

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

$$\left(b^{-3}\right)^{-2}\left(c^{-7}\right)^{-2}\left(b^{3}\right)^{-3}\left(c^{-2}\right)^{-3}$$

Use the Commutative Property of Multiplication.

$$\left(b^{-3}\right)^{-2}\left(b^{3}\right)^{-3}\left(c^{-7}\right)^{-2}\left(c^{-2}\right)^{-3}$$

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

$$b^{-3\left(-2\right)}b^{3\left(-3\right)}c^{-7\left(-2\right)}c^{-2\left(-3\right)}$$

Multiply -3 times -2.

$$b^{6}b^{3\left(-3\right)}c^{-7\left(-2\right)}c^{-2\left(-3\right)}$$

Multiply 3 times -3.

$$b^{6}b^{-9}c^{-7\left(-2\right)}c^{-2\left(-3\right)}$$

Multiply -7 times -2.

$$b^{6}b^{-9}c^{14}c^{-2\left(-3\right)}$$

Multiply -2 times -3.

$$b^{6}b^{-9}c^{14}c^{6}$$

To multiply powers of the same base, add their exponents.

$$b^{6-9}c^{14+6}$$

Add the exponents 6 and -9.

$$b^{-3}c^{14+6}$$

Add the exponents 14 and 6.

$$b^{-3}c^{20}$$

Expand

$$\frac{c^{20}}{b^{3}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(b^{-3}c^{-7}\right)^{-2}\left(b^{3}c^{-2}\right)^{-3}$$

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

$$\left(b^{-3}\right)^{-2}\left(c^{-7}\right)^{-2}\left(b^{3}\right)^{-3}\left(c^{-2}\right)^{-3}$$

Use the Commutative Property of Multiplication.

$$\left(b^{-3}\right)^{-2}\left(b^{3}\right)^{-3}\left(c^{-7}\right)^{-2}\left(c^{-2}\right)^{-3}$$

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

$$b^{-3\left(-2\right)}b^{3\left(-3\right)}c^{-7\left(-2\right)}c^{-2\left(-3\right)}$$

Multiply -3 times -2.

$$b^{6}b^{3\left(-3\right)}c^{-7\left(-2\right)}c^{-2\left(-3\right)}$$

Multiply 3 times -3.

$$b^{6}b^{-9}c^{-7\left(-2\right)}c^{-2\left(-3\right)}$$

Multiply -7 times -2.

$$b^{6}b^{-9}c^{14}c^{-2\left(-3\right)}$$

Multiply -2 times -3.

$$b^{6}b^{-9}c^{14}c^{6}$$

To multiply powers of the same base, add their exponents.

$$b^{6-9}c^{14+6}$$

Add the exponents 6 and -9.

$$b^{-3}c^{14+6}$$

Add the exponents 14 and 6.

$$b^{-3}c^{20}$$