Solve ((2a ^ 3 * b ^ 2 * c ^ 0)/(3a ^ 2 * b ^ 3 * c ^ 7)) ^ - 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

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

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

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

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

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 $\frac{1}{9}$.

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