(25-4-) 2

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Topic Video
Question

Simplify the expression. Assume all variables are positive. 

The given expression for problem number 27 is:

\[
(25^{\frac{3}{2}} \cdot 4^{-\frac{3}{4}})^2
\]

This mathematical expression involves exponentiation and multiplication:

1. **Inside the Parentheses**:
   - \(25^{\frac{3}{2}}\) means 25 raised to the power of \( \frac{3}{2} \).
   - \(4^{-\frac{3}{4}}\) means 4 raised to the power of \(-\frac{3}{4}\).

2. **Outer Squaring**:
   - The entire product inside the parentheses is squared, as indicated by the exponent 2 outside the parentheses.

This type of expression is often explored in algebra and precalculus topics related to exponents and powers. It can be simplified further by calculating the powers and carrying out the multiplication.
Transcribed Image Text:The given expression for problem number 27 is: \[ (25^{\frac{3}{2}} \cdot 4^{-\frac{3}{4}})^2 \] This mathematical expression involves exponentiation and multiplication: 1. **Inside the Parentheses**: - \(25^{\frac{3}{2}}\) means 25 raised to the power of \( \frac{3}{2} \). - \(4^{-\frac{3}{4}}\) means 4 raised to the power of \(-\frac{3}{4}\). 2. **Outer Squaring**: - The entire product inside the parentheses is squared, as indicated by the exponent 2 outside the parentheses. This type of expression is often explored in algebra and precalculus topics related to exponents and powers. It can be simplified further by calculating the powers and carrying out the multiplication.
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