Solve {left(-2a^3b^2c^0/3a^2{b^3{c}^7}right)}^-2

$${ \left( \frac{ -2 { a }^{ 3 } { b }^{ 2 } { c }^{ 0 } }{ 3 { a }^{ 2 } { b }^{ 3 } { c }^{ 7 } } \right) }^{ -2 }$$

Evaluate

$$\frac{9\times \left(\frac{b}{a}\right)^{2}c^{14}}{4}$$

Solution Steps

Cancel out a^{2}b^{2} in both numerator and denominator.

$$\left(\frac{-2ac^{0}}{3bc^{7}}\right)^{-2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{-2a}{3bc^{7}}\right)^{-2}$$

To raise \frac{-2a}{3bc^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2a\right)^{-2}}{\left(3bc^{7}\right)^{-2}}$$

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

$$\frac{\left(-2\right)^{-2}a^{-2}}{\left(3bc^{7}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}a^{-2}}{\left(3bc^{7}\right)^{-2}}$$

Expand \left(3bc^{7}\right)^{-2}.

$$\frac{\frac{1}{4}a^{-2}}{3^{-2}b^{-2}\left(c^{7}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{\frac{1}{4}a^{-2}}{3^{-2}b^{-2}c^{-14}}$$

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

$$\frac{\frac{1}{4}a^{-2}}{\frac{1}{9}b^{-2}c^{-14}}$$

Expand

$$\frac{9\times \left(\frac{b}{a}\right)^{2}c^{14}}{4}$$

Solution Steps

Cancel out a^{2}b^{2} in both numerator and denominator.

$$\left(\frac{-2ac^{0}}{3bc^{7}}\right)^{-2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{-2a}{3bc^{7}}\right)^{-2}$$

To raise \frac{-2a}{3bc^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2a\right)^{-2}}{\left(3bc^{7}\right)^{-2}}$$

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

$$\frac{\left(-2\right)^{-2}a^{-2}}{\left(3bc^{7}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}a^{-2}}{\left(3bc^{7}\right)^{-2}}$$

Expand \left(3bc^{7}\right)^{-2}.

$$\frac{\frac{1}{4}a^{-2}}{3^{-2}b^{-2}\left(c^{7}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

$$\frac{\frac{1}{4}a^{-2}}{3^{-2}b^{-2}c^{-14}}$$

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

$$\frac{\frac{1}{4}a^{-2}}{\frac{1}{9}b^{-2}c^{-14}}$$