Math Problem Statement

(x^2)(x^5)

Solution

The expression to simplify is:

(x2)(x5)(x^2)(x^5)

To simplify this, use the product of powers property, which states that when multiplying two exponents with the same base, you add the exponents. In this case, the base is xx, so we add the exponents 22 and 55:

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

Thus, the simplified expression is:

x7x^7

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:

  1. How do you simplify (x3)(x4)(x^3)(x^4)?
  2. What happens if the exponents are negative, like (x2)(x5)(x^{-2})(x^5)?
  3. How do you simplify expressions like (x2)(y5)(x^2)(y^5) where the bases are different?
  4. What is the rule for dividing exponents with the same base, like x5x2\frac{x^5}{x^2}?
  5. How do you handle powers of powers, like (x3)2(x^3)^2?

Tip: Always remember that the base of the powers must be the same to apply the product or quotient of powers rules.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Product of Powers Rule

Formulas

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

Theorems

Product of Powers Property

Suitable Grade Level

Grades 7-9