Pregunta
Write
using rational exponents.
B. 16
C.
D.
B. 16
C.
D.
Ask by Turnbull Gonzalez. in the United States
Jan 30,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The correct expression using rational exponents is
, which equals 256.
Solución
To express
using rational exponents, follow these steps:
-
Rewrite the Square Root as an Exponent:The square root of 16 can be written as
. -
Express 16 in Terms of Base 4:Since
, substitute this into the equation: -
Combine the Exponents:Now, multiply
by : -
Final Expression:Therefore,
expressed with rational exponents is: -
Evaluate
(Optional): For completeness, calculating:
Review of Provided Options:
Given the choices:
- A.
- B. 16
- C.
- D.
None of these options correctly represent
. The correct expression using rational exponents is
, which equals 256.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
Did you know that the expression
can be simplified to have a more manageable form? First, we can rewrite that pesky square root as a rational exponent! Since
, we combine the exponents. So,
. To express
with rational exponents, remember
itself can be written as
, ensuring everything fits neatly into the world of exponents!
Now, let’s dive into the world of rational exponents! Here’s a fun fact: rational exponents can express roots. For example, instead of writing
, you can write it using exponents as
. So for any number
,
represents the n-th root of
, leading to exciting explorations in algebra and beyond. Keep this in mind, and your math journey will be filled with joy!
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