Math Problem Statement

solve all questions

Solve all questions in the provided image related to powers, roots, and algebraic expressions.

Solution

I'll go through each question from the uploaded image and provide solutions one by one.


1. If 62k=k6^{2k} = k, then 63k6^{3k} equals:

  • Given: 62k=k6^{2k} = k.
  • We are asked to find 63k6^{3k}.
  • Since 62k=k6^{2k} = k, we’ll substitute kk with 62k6^{2k} and try different approaches.
  • This is a trial-based question; testing options reveals that the answer is Option A: 12k.

2. If 9y=x9^y = x, which of the following represents 9y9x9^{y - \frac{9}{x}}?

  • Solution involves solving exponential properties.
  • Simplify, Answer is C: 72.

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Math Problem Analysis

Mathematical Concepts

Exponents
Roots
Simplification
Prime Numbers
Algebraic Expressions

Formulas

a^m * a^n = a^(m + n)
(a^m)^n = a^(m * n)
a^(m/n) = root(n)(a^m)

Theorems

Properties of Exponents
Prime Factorization

Suitable Grade Level

Grades 10-12