How to solve a ( c ) b

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve a ( c ) b | Equatix

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Question

$$( \frac { x ^ { a } } { x ^ { b } } ) ^ { 2 } ( \frac { x ^ { b } } { x ^ { c } } ) ^ { 2 } ( \frac { x ^ { c } } { x ^ { a } } ) ^ { 2 }$$

Evaluate

$1$

Solution Steps

To raise $\frac{x^{a}}{x^{b}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{a}\right)^{2}}{\left(x^{b}\right)^{2}}\times \left(\frac{x^{b}}{x^{c}}\right)^{2}\times \left(\frac{x^{c}}{x^{a}}\right)^{2}$$

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

$$\frac{\left(x^{a}\right)^{2}}{\left(x^{b}\right)^{2}}\times \frac{\left(x^{b}\right)^{2}}{\left(x^{c}\right)^{2}}\times \left(\frac{x^{c}}{x^{a}}\right)^{2}$$

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

$$\frac{\left(x^{a}\right)^{2}}{\left(x^{b}\right)^{2}}\times \frac{\left(x^{b}\right)^{2}}{\left(x^{c}\right)^{2}}\times \frac{\left(x^{c}\right)^{2}}{\left(x^{a}\right)^{2}}$$

Multiply $\frac{\left(x^{a}\right)^{2}}{\left(x^{b}\right)^{2}}$ times $\frac{\left(x^{b}\right)^{2}}{\left(x^{c}\right)^{2}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{a}\right)^{2}\left(x^{b}\right)^{2}}{\left(x^{b}\right)^{2}\left(x^{c}\right)^{2}}\times \frac{\left(x^{c}\right)^{2}}{\left(x^{a}\right)^{2}}$$

Cancel out $\left(x^{b}\right)^{2}$ in both numerator and denominator.

$$\frac{\left(x^{a}\right)^{2}}{\left(x^{c}\right)^{2}}\times \frac{\left(x^{c}\right)^{2}}{\left(x^{a}\right)^{2}}$$

Multiply $\frac{\left(x^{a}\right)^{2}}{\left(x^{c}\right)^{2}}$ times $\frac{\left(x^{c}\right)^{2}}{\left(x^{a}\right)^{2}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{a}\right)^{2}\left(x^{c}\right)^{2}}{\left(x^{c}\right)^{2}\left(x^{a}\right)^{2}}$$

Cancel out $\left(x^{a}\right)^{2}\left(x^{c}\right)^{2}$ in both numerator and denominator.

$$1$$

Show Solution

Factor

$1$