Math Problem Statement

Simplify the expression (x^2 * x^5) / x^3.

Solution

The expression in the image appears to be:

x2x5x3\frac{x^2 \cdot x^5}{x^3}

To simplify this expression, we can combine the powers of xx in the numerator. The multiplication of exponents with the same base follows the rule xaxb=xa+bx^a \cdot x^b = x^{a+b}, so:

x2x5=x2+5=x7x^2 \cdot x^5 = x^{2+5} = x^7

Now the expression becomes:

x7x3\frac{x^7}{x^3}

Next, applying the division rule for exponents xaxb=xab\frac{x^a}{x^b} = x^{a-b}, we subtract the exponents:

x7x3=x73=x4\frac{x^7}{x^3} = x^{7-3} = x^4

Thus, the simplified expression is:

x4x^4

Let me know if you need further clarification or details!


Would you like further explanation on exponent rules? Here are some related questions you could explore:

  1. What is the rule for dividing exponents with the same base?
  2. How do you simplify expressions with negative exponents?
  3. What happens when you raise a product to an exponent?
  4. How can exponents be applied in polynomial equations?
  5. How do you handle fractional exponents in expressions?

Tip: When multiplying powers of the same base, always add the exponents; when dividing, subtract them!

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Simplifying Expressions

Formulas

x^a * x^b = x^(a+b)
x^a / x^b = x^(a-b)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 7-9