Math Problem Statement

2^-2m^-3/n^0

Solution

The given expression is:

22m3÷n02^{-2} m^{-3} \div n^0

Let's break it down:

  1. 222^{-2}: This means 22 raised to the power of 2-2. Any number raised to a negative exponent is the reciprocal of that number raised to the positive exponent: 22=122=142^{-2} = \frac{1}{2^2} = \frac{1}{4}

  2. m3m^{-3}: This means mm raised to the power of 3-3. Similarly, a negative exponent means the reciprocal: m3=1m3m^{-3} = \frac{1}{m^3}

  3. n0n^0: Any non-zero number raised to the power of zero is equal to 1: n0=1n^0 = 1

Now, combining all these results:

14×1m3÷1=14m3\frac{1}{4} \times \frac{1}{m^3} \div 1 = \frac{1}{4m^3}

So, the simplified expression is:

14m3\frac{1}{4m^3}

Would you like any further explanation or have additional questions on this?

Here are some related questions to explore:

  1. How do negative exponents behave in expressions?
  2. What are the rules for dividing terms with exponents?
  3. What does the zero exponent rule tell us about any non-zero number raised to the power of zero?
  4. How would you simplify expressions with multiple terms having negative exponents?
  5. Can you apply this simplification process to more complex algebraic expressions?

Tip: Remember, negative exponents can always be rewritten as fractions, and anything raised to the power of zero (except zero itself) equals 1.

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents
Zero Exponent Rule
Simplification

Formulas

a^(-n) = 1/a^n
a^0 = 1 (for a ≠ 0)

Theorems

Negative exponent rule
Zero exponent rule

Suitable Grade Level

Grades 7-9