Simplifying Exponents in Math Made Easy
Question 1: What is the result of raising 5 to the power of -2 times 3 to the power of 5, all raised to the power of -2?
A. 3 raised to the third power divided by 5 raised to the fourth power
B. Negative 3 raised to the third power divided by 5 raised to the fourth power
C. 5 raised to the fourth power divided by 3 raised to the tenth power
D. Negative 5 raised to the fourth power divided by 3 raised to the tenth power
Answer 1:
The expression is equivalent to 625.
When simplifying expressions involving exponents, it is important to apply the laws of exponents correctly.
In this particular case, the expression (5^-2 * 3^5)^-2 simplifies to 625.
To simplify, first evaluate the exponents inside the parentheses: 5^-2 is equal to 1/5^2 which is 1/25, and 3^5 is equal to 243.
Next, raise the result to the -2 power: (1/25)^-2 = (25/1)^2 = 625.
Therefore, the final answer to the expression is 625.