Solve frac{-15a^{30}b^{8}c^{2}z^{4}}{-3a^7b^6z^2}text{es}5a^2

$$\frac { - 15 a ^ { 30 } b ^ { 8 } c ^ { 2 } z ^ { 4 } } { - 3 a ^ { 7 } b ^ { 6 } z ^ { 2 } } \text { es } 5 a ^ { 2 }$$

Evaluate

$$25es\left(bcz\right)^{2}a^{25}$$

Solution Steps

Cancel out 3z^{2}b^{6}a^{7} in both numerator and denominator.

$$\frac{-5b^{2}c^{2}z^{2}a^{23}}{-1}es\times 5a^{2}$$

Anything divided by -1 gives its opposite.

$$5b^{2}c^{2}z^{2}a^{23}es\times 5a^{2}$$

Multiply 5 and 5 to get 25.

$$25b^{2}c^{2}z^{2}a^{23}esa^{2}$$

To multiply powers of the same base, add their exponents. Add 23 and 2 to get 25.

$$25b^{2}c^{2}z^{2}a^{25}es$$

Differentiate w.r.t. z

$$50esz\left(bc\right)^{2}a^{25}$$