Math Problem Statement

Exponent rules worksheet with multiple problems involving multiplying, dividing, and simplifying exponent expressions.

Solution

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Here's a breakdown of the visible problems:

  1. (18)5(18)3\left( \frac{1}{8} \right)^5 \left( \frac{1}{8} \right)^3
  2. 3k54k53k^5 \cdot 4k^5
  3. 45k115k3\frac{45k^{11}}{5k^3}
  4. 18h86h3\frac{18h^8}{6h^3}
  5. (3d7n)(3d^7n)
  6. (2x25x7)(2x^2 \cdot 5x^7)
  7. 3f9\frac{3}{f^9}
  8. 2c0=92c^0 = 9
  9. 9m2x3\frac{9m^2}{x^3}
  10. (x2y2z)2(x^2y^2z)^2

Would you like detailed solutions for these, or is there a particular problem you'd like to focus on first?

Here are five follow-up questions you might consider based on exponent rules:

  1. How do you simplify expressions that involve multiplying terms with the same base?
  2. What rule governs dividing terms with the same base but different exponents?
  3. How does raising a power to another power affect the exponent?
  4. Why does any number raised to the power of 0 equal 1, except for 0 itself?
  5. How do you simplify expressions where the base is a product or quotient of variables?

Tip: Always remember that when multiplying terms with the same base, you add their exponents (e.g., aman=am+na^m \cdot a^n = a^{m+n}).

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Math Problem Analysis

Mathematical Concepts

Exponent Rules
Algebra
Simplifying Expressions

Formulas

a^m * a^n = a^(m+n)
(a^m)/(a^n) = a^(m-n)
(a^m)^n = a^(m*n)
a^0 = 1

Theorems

Properties of Exponents

Suitable Grade Level

Grades 7-9