Question

IMPORTANT: every " a, b, c and + , -" are meant to be exponents

Answer 1

The expression $(\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}$ is an algebraic expression, and the result of simplifying the expression $(\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}$ is 1

How to simplify the expression?

The expression is given as:

$(\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}$

Apply the power rule of indices

$(x^{a-b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}$

Expand the exponents of the expression

$x^{a^2-b^2} \cdot x^{b^2 - c^2} \cdot x^{c^2 - a^2$

Apply the product rule of indices

$x^{a^2-b^2+b^2 - c^2+c^2 - a^2$

Collect like terms

$x^{a^2- a^2-b^2+b^2 - c^2+c^2$

Evaluate the differences

$x^{0-0 - 0$

This gives

$x^{0$

Evaluate the exponent

1

Hence, the result of simplifying the expression $(\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}$ is 1

Read more about simplifying expressions at:

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