Simplify (x^3 * x^5)/x^2, where x != 0.

Solution

Algebra · Medium

Use the product rule for exponents in the numerator. When multiplying powers with the same base, add the exponents:
x^3 * x^5 = x^(3 + 5) = x^8

Now divide powers with the same base. When dividing, subtract the exponent in the denominator from the exponent in the numerator:
x^8/x^2 = x^(8 - 2)

Simplify:
x^6

The restriction x != 0 remains because the original expression has x^2 in the denominator.

Result

x^6, where x != 0