Math Problem Statement

(27^3/9^5)

Solution

Let's solve the expression 27395\frac{27^3}{9^5}.

  1. First, we can express 27 and 9 in terms of powers of 3: 27=33and9=3227 = 3^3 \quad \text{and} \quad 9 = 3^2 So, the expression becomes: (33)3(32)5\frac{(3^3)^3}{(3^2)^5}

  2. Simplify the exponents: 33×332×5=39310\frac{3^{3 \times 3}}{3^{2 \times 5}} = \frac{3^9}{3^{10}}

  3. Apply the property of exponents aman=amn\frac{a^m}{a^n} = a^{m-n}: 3910=313^{9-10} = 3^{-1}

  4. Simplify further: 31=133^{-1} = \frac{1}{3}

So, the final answer is 13\frac{1}{3}.

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:

  1. What is the result of 812273\frac{81^2}{27^3}?
  2. How do you simplify 16446\frac{16^4}{4^6}?
  3. What is 9329^{\frac{3}{2}} in simplified form?
  4. How do you calculate 1252254\frac{125^2}{25^4}?
  5. How do you simplify expressions with negative exponents?

Tip: When simplifying expressions with exponents, always look for a common base to make the process easier!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponents
Fractional Exponents

Formulas

Exponent rules
Fractional exponent simplification

Theorems

-

Suitable Grade Level

Grades 9-12