Solve a^{-6}*b^{5}*c^-7*a^-2*b^9*c^4

$$a ^ { - 6 } \cdot b ^ { 5 } \cdot c ^ { - 7 } \cdot a ^ { - 2 } \cdot b ^ { 9 } \cdot c ^ { 4 }$$

Evaluate

$$\frac{b^{14}}{c^{3}a^{8}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$a^{-6}b^{5}c^{-7}a^{-2}b^{9}c^{4}$$

Use the Commutative Property of Multiplication.

$$a^{-6}a^{-2}b^{5}b^{9}c^{-7}c^{4}$$

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

$$a^{-6-2}b^{5+9}c^{-7+4}$$

Add the exponents -6 and -2.

$$a^{-8}b^{5+9}c^{-7+4}$$

Raise a to the power -8.

$$\frac{1}{a^{8}}b^{5+9}c^{-7+4}$$

Add the exponents 5 and 9.

$$\frac{1}{a^{8}}b^{14}c^{-7+4}$$

Add the exponents -7 and 4.

$$\frac{1}{a^{8}}b^{14}c^{-3}$$

Multiply \frac{1}{a^{6}} times \frac{1}{a^{2}}.

$$\frac{1}{a^{8}}b^{14}\times \frac{1}{c^{3}}$$

Differentiate w.r.t. a

$$-\frac{8b^{14}}{c^{3}a^{9}}$$