Question

Solve this equation.

Answer 1

`(4a^6b^5)/(c^3)`

Explanation:

Given expression:

`(8a^4b^(-3)c^(12))/(2a^(-2)b^(-8)c^(15))`

Separate like terms:

`(8)/(2) \cdot (a^4)/(a^(-2))\cdot (b^(-3))/(b^(-8)) \cdot (c^(12))/(c^(15))`

Divide the numbers:

`4\cdot (a^4)/(a^(-2))\cdot (b^(-3))/(b^(-8)) \cdot (c^(12))/(c^(15))`

`\textsf{Apply the exponent rule} \quad (a^b)/(a^c)=a^(b-c):`

`4 \cdot a^(4-(-2)) \cdot b^(-3-(-8)) \cdot c^(12-15)`

Simplify the exponents:

`4 \cdot a^6 \cdot b^5 \cdot c^(-3)`

`\textsf{Apply the exponent rule} \quad a^(-n)=(1)/(a^n):`

`4 \cdot a^6 \cdot b^5 \cdot (1)/(c^3)`

Simplify:

`(4a^6b^5)/(c^3)`