f What is the simplified expression for 5 to the power of negative 3 multiplied by 2 to the power of 2 multiplied by 5 to the power of 6 whole over 2 to the power of 3 multiplied by 5 to the power of 2?
//5^-3 = 1/(5^3)
(2^25^6)/(5^32^35^2)=
(2^22^-3)(5^65^-35^-2)=
(2^-1)(5^1)=
5/2=
2.5=
Answer:
The simplified expression is: \(\frac{5}{2}\).
Step-by-step explanation:
We have been given an expression:
\(\frac{5^{-3}\cdot 2^2\cdot 5^6}{2^3\cdot 5^2}\)
We will simplify it by adding powers of the terms which have same base
So first we will simplify numerator and denominator individually so we get:
\(\frac{5^3\cdot 2^2}{2^3\cdot 5^2}\)
Cancel the powers of the term with same base
\(\Rightarrow \frac{5}{2}\)
Hence, the simplified expression of:
\(\frac{5^{-3}\cdot 2^2\cdot 5^6}{2^3\cdot 5^2}=\frac{5}{2}\).