Solve (frac{3a^{2}c^{5}}{-4ac^6})^-2*(5a/c^3)^3

$$( \frac { 3 a ^ { 2 } c ^ { 5 } } { - 4 a c ^ { 6 } } ) ^ { - 2 } \cdot ( \frac { 5 a } { c ^ { 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{2000a}{9c^{7}}$$

Solution Steps

Cancel out ac^{5} in both numerator and denominator.

$$\left(\frac{3a}{-4c}\right)^{-2}\times \left(\frac{5a}{c^{3}}\right)^{3}$$

To raise \frac{3a}{-4c} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3a\right)^{-2}}{\left(-4c\right)^{-2}}\times \left(\frac{5a}{c^{3}}\right)^{3}$$

To raise \frac{5a}{c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3a\right)^{-2}}{\left(-4c\right)^{-2}}\times \frac{\left(5a\right)^{3}}{\left(c^{3}\right)^{3}}$$

Multiply \frac{\left(3a\right)^{-2}}{\left(-4c\right)^{-2}} times \frac{\left(5a\right)^{3}}{\left(c^{3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3a\right)^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}\left(c^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(3a\right)^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Expand \left(3a\right)^{-2}.

$$\frac{3^{-2}a^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}a^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Expand \left(5a\right)^{3}.

$$\frac{\frac{1}{9}a^{-2}\times 5^{3}a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\frac{1}{9}a^{-2}\times 125a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Multiply \frac{1}{9} and 125 to get \frac{125}{9}.

$$\frac{\frac{125}{9}a^{-2}a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$\frac{\frac{125}{9}a^{1}}{\left(-4c\right)^{-2}c^{9}}$$

Expand \left(-4c\right)^{-2}.

$$\frac{\frac{125}{9}a^{1}}{\left(-4\right)^{-2}c^{-2}c^{9}}$$

Calculate -4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{125}{9}a^{1}}{\frac{1}{16}c^{-2}c^{9}}$$

To multiply powers of the same base, add their exponents. Add -2 and 9 to get 7.

$$\frac{\frac{125}{9}a^{1}}{\frac{1}{16}c^{7}}$$

Calculate a to the power of 1 and get a.

$$\frac{\frac{125}{9}a}{\frac{1}{16}c^{7}}$$

Expand

$$\frac{2000a}{9c^{7}}$$

Solution Steps

Cancel out ac^{5} in both numerator and denominator.

$$\left(\frac{3a}{-4c}\right)^{-2}\times \left(\frac{5a}{c^{3}}\right)^{3}$$

To raise \frac{3a}{-4c} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3a\right)^{-2}}{\left(-4c\right)^{-2}}\times \left(\frac{5a}{c^{3}}\right)^{3}$$

To raise \frac{5a}{c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3a\right)^{-2}}{\left(-4c\right)^{-2}}\times \frac{\left(5a\right)^{3}}{\left(c^{3}\right)^{3}}$$

Multiply \frac{\left(3a\right)^{-2}}{\left(-4c\right)^{-2}} times \frac{\left(5a\right)^{3}}{\left(c^{3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3a\right)^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}\left(c^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(3a\right)^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Expand \left(3a\right)^{-2}.

$$\frac{3^{-2}a^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}a^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Expand \left(5a\right)^{3}.

$$\frac{\frac{1}{9}a^{-2}\times 5^{3}a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\frac{1}{9}a^{-2}\times 125a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

Multiply \frac{1}{9} and 125 to get \frac{125}{9}.

$$\frac{\frac{125}{9}a^{-2}a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$\frac{\frac{125}{9}a^{1}}{\left(-4c\right)^{-2}c^{9}}$$

Expand \left(-4c\right)^{-2}.

$$\frac{\frac{125}{9}a^{1}}{\left(-4\right)^{-2}c^{-2}c^{9}}$$

Calculate -4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{125}{9}a^{1}}{\frac{1}{16}c^{-2}c^{9}}$$

To multiply powers of the same base, add their exponents. Add -2 and 9 to get 7.

$$\frac{\frac{125}{9}a^{1}}{\frac{1}{16}c^{7}}$$

Calculate a to the power of 1 and get a.

$$\frac{\frac{125}{9}a}{\frac{1}{16}c^{7}}$$