Podcast
Questions and Answers
What is the simplified value of $x$ when $x = rac{(3^2)}{(2^2)} imes rac{(2^4)}{(3^4)}$?
What is the simplified value of $x$ when $x = rac{(3^2)}{(2^2)} imes rac{(2^4)}{(3^4)}$?
- $ rac{3^6}{2^6}$
- $ rac{27}{16}$
- $ rac{9}{4}$
- $ rac{3}{2}$ (correct)
How is $x^{-2}$ expressed using the properties of exponents?
How is $x^{-2}$ expressed using the properties of exponents?
- $ rac{1}{x^2}$ (correct)
- $ rac{3^{-12}}{2^{-12}}$
- $(-x)^2$
- $x^4$
Which of the following represents the correct calculation of $x^{-2}$ if $x = rac{3^6}{2^6}$?
Which of the following represents the correct calculation of $x^{-2}$ if $x = rac{3^6}{2^6}$?
- $ rac{2^{12}}{3^{12}}$ (correct)
- $ rac{3^{-12}}{2^{-12}}$
- $ rac{3^{12}}{2^{12}}$
- $ rac{2^{6}}{3^{6}}$
What happens to the base when applying the exponent $x^{-2}$ to $x = rac{3}{2}$?
What happens to the base when applying the exponent $x^{-2}$ to $x = rac{3}{2}$?
Given $x = rac{3^6}{2^6}$, what is the value of $(2/3)^{12}$ in relation to $x^{-2}$?
Given $x = rac{3^6}{2^6}$, what is the value of $(2/3)^{12}$ in relation to $x^{-2}$?
Flashcards
Exponent rule for multiplication
Exponent rule for multiplication
When multiplying terms with the same base, add the exponents.
Negative exponent rule
Negative exponent rule
A term raised to a negative exponent is equal to one divided by the term raised to the positive exponent.
x = (3/2)^6
x = (3/2)^6
Result of simplifying (3/2)^2 * (2/3)^-4
x^(-2)
x^(-2)
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Correct option for x^(-2)
Correct option for x^(-2)
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Study Notes
Problem 63
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Given the equation x = (3/2)² × (2/3)⁻⁴
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Find the value of x⁻²
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Solution:
- x = (3/2)² × (2/3)⁻⁴
- Using the rule a⁻ⁿ = 1/aⁿ
- x = (3/2)² × (3/2)⁴
- x = (3/2)²⁺⁴ = (3/2)⁶
- x⁻² = 1/x² = (2/3)¹²
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Description
This quiz covers properties of exponents and simplification of fractional expressions, focusing on the calculation of $x$ as well as $x^{-2}$. It explores how to express negative exponents using the quotient of bases and determines the value of expressions relating to given values of $x$. Test your understanding of these concepts with this engaging quiz.
