Answer:
1. [tex]4x^{10}y^{11}[/tex]
2. [tex]y=5.25[/tex]
Step-by-step explanation:
Question 1.
Given:
[tex]\frac{(4x^4y^5)^4}{(4x^2y^3)^3}[/tex]
We need to Simplify given expression we get;
Solution:
Now we know that;
By Using Law of Indices which states;
[tex](x^m)^n=x^{m.n}[/tex]
So we get:
[tex]\frac{4^4x^{4\times4}y^{5\times4}}{4^3x^{2\times3}y^{3\times3}}\\\\\frac{4^4x^{16}y^{20}}{4^3x^{6}y^{9}}[/tex]
Now Again By Law of Indices we get;
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
So we get:
[tex]=4^{(4-3)}x^{(16-6)}y^{(20-9)}\\\\=4x^{10}y^{11}[/tex]
Hence Simplified expression is [tex]4x^{10}y^{11}[/tex].
Question 2.
Given:
[tex](27)^{(2y-2)}=(3)^{(2y+15)}[/tex]
We need to solve for 'y'.
Solution:
To find 'y' we need to first make the base same.
Now we know that;
[tex]27 = 3\times3\times3 = 3^3[/tex]
So we can say that:
[tex](3)^{3(2y-2)}=(3)^{2y+15}[/tex]
Now Applying Distributive property we get;
[tex](3)^{6y-6}=(3)^{2y+15}[/tex]
Now we can say that;
When an expression has equal bases then their exponent are said to equal too.
from above we get;
[tex]6y-6=2y+15[/tex]
Combing like terms we get;
[tex]6y-2y=15+6\\\\4y=21[/tex]
Dividing both side by 2 we get;
[tex]\frac{4y}{4}=\frac{21}{4}\\\\y=5.25[/tex]
Hence The Value of y is 5.25.
