Math Problem Statement

Solve and understand various problems related to exponents, including determining bases, calculating powers, and simplifying exponential expressions.

Solution

The document you've uploaded contains a worksheet on the topic of Exponents (Eksponen). It includes exercises on identifying base numbers and exponents, calculating exponent values, and simplifying exponential expressions.

Here is a summary of the key sections:

Competencies:

  1. Understanding the concept of exponents.
  2. Calculating values of numbers with exponents.
  3. Applying the properties of exponents.

Exercises:

  1. Identifying Exponents:

    • Convert expressions into exponent form, such as 2×22 \times 2 becoming 222^2.
    • Example:
      • 2×2=222 \times 2 = 2^2
      • 2×2×2=232 \times 2 \times 2 = 2^3
  2. Determine the Base and Exponent:

    • A table where you are asked to identify the base and exponent from given exponential expressions like 545^4, 646^4, etc.
  3. Calculate Powers:

    • Calculate powers such as 545^4 and (12)4\left( \frac{1}{2} \right)^4.
  4. Simplifying Exponent Expressions:

    • Simplify expressions like 37÷333^7 \div 3^3 and other more complex forms such as (2133)2\left( 2^{-1} \cdot 3^3 \right)^2.
  5. Further Operations with Exponents:

    • Convert expressions like 63/56^{3/5}, calculate powers such as 163/416^{3/4}, and simplify complex exponential forms like (2764)2/3\left( \frac{27}{64} \right)^{2/3}.

Do you want a step-by-step explanation for any of these questions or help with specific problems? Feel free to ask!


5 Related Questions:

  1. How do you simplify an expression like 37÷333^7 \div 3^3?
  2. What is the result of (12)4\left( \frac{1}{2} \right)^4?
  3. How do you convert a fractional exponent like 63/56^{3/5} to a radical form?
  4. How do you simplify the expression (2133)2\left( 2^{-1} \cdot 3^3 \right)^2?
  5. What steps are involved in calculating (2764)2/3\left( \frac{27}{64} \right)^{2/3}?

Tip: Remember that when dividing powers with the same base, subtract the exponents: am÷an=amna^m \div a^n = a^{m-n}.

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Math Problem Analysis

Mathematical Concepts

Exponents
Simplification
Fractional Exponents
Radical Forms

Formulas

a^m / a^n = a^(m-n)
(a^m)^n = a^(m*n)
(ab)^n = a^n * b^n
a^(-n) = 1/a^n
x^(1/n) = n-th root of x

Theorems

Laws of Exponents

Suitable Grade Level

Grades 7-9