Math Problem Statement

(5/3)^-2

Solution

The image shows the expression:

(53)2\left(\frac{5}{3}\right)^{-2}

To solve this, we follow these steps:

  1. The negative exponent rule states that an=1ana^{-n} = \frac{1}{a^n}.
  2. Apply this rule to the expression:

(53)2=1(53)2\left(\frac{5}{3}\right)^{-2} = \frac{1}{\left(\frac{5}{3}\right)^2}

  1. Now, square the fraction:

(53)2=5232=259\left(\frac{5}{3}\right)^2 = \frac{5^2}{3^2} = \frac{25}{9}

  1. So the expression becomes:

1259=925\frac{1}{\frac{25}{9}} = \frac{9}{25}

Thus, the value of (53)2=925\left(\frac{5}{3}\right)^{-2} = \frac{9}{25}.

Would you like more details or clarification on any part of this process?

Here are five related questions:

  1. How do you simplify expressions with negative exponents?
  2. What happens when both the numerator and denominator of a fraction have negative exponents?
  3. How can you verify your answer when simplifying fractions with exponents?
  4. What are some applications of exponent rules in real-world problems?
  5. How do exponents impact the behavior of functions?

Tip: Always check if a fraction can be simplified after applying exponent rules!

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Math Problem Analysis

Mathematical Concepts

Exponents
Fractions

Formulas

a^(-n) = 1/a^n
(a/b)^n = a^n / b^n

Theorems

Exponent rules

Suitable Grade Level

Grades 7-9