Math Problem Statement

Rewrite using a single positive exponentz; 4^-2/4^-7

Solution

We have the expression:

4247\frac{4^{-2}}{4^{-7}}

Step 1: Apply the Quotient Rule of Exponents

The quotient rule states that:

aman=amn\frac{a^m}{a^n} = a^{m-n}

Applying this to our expression:

42(7)=42+7=454^{-2 - (-7)} = 4^{-2 + 7} = 4^5

Final Answer:

454^5

Would you like a deeper explanation or examples?

Here are some related questions:

  1. Simplify 3439\frac{3^{-4}}{3^{-9}} using a single exponent.
  2. Express 53×565^{-3} \times 5^6 with a single exponent.
  3. Rewrite x5x2\frac{x^5}{x^{-2}} using only positive exponents.
  4. What is the value of 23×252^{-3} \times 2^5?
  5. Convert 102105\frac{10^{-2}}{10^{-5}} to a positive exponent.

Tip: When dividing powers with the same base, subtract the exponents!

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Math Problem Analysis

Mathematical Concepts

Exponents
Exponent Rules
Quotient Rule of Exponents

Formulas

\frac{a^m}{a^n} = a^{m-n}

Theorems

Quotient Rule of Exponents

Suitable Grade Level

Grades 6-8