Answer with explanation:
1.→Answer Written by Jack is Incorrect.
[tex]m^n=\text{exponent}\\\\\frac{x^a}{x^b}=x^{a-b}\\\\x^a \times x^b=x^{a+b}[/tex]
Error:Instead of subtracting powers,jack has added powers of same exponent.
Correct Solution:
[tex]=\frac{54\times x^9 \times y^8}{6\times x^3 \times y^4}\\\\ \text{Here ,correct answer should be}=9\times x^{9-3} \times y^{8-4}\\\\=9 x^6 y^4[/tex]
2.Initial Amount, a=78,000
Rate =3 %=0.03
Error: Rate percent should be divided by 100, to get the value of b.
So, b= 0.03
Correct Solution:
Exponential growth is given by
[tex]y=a\times b^x\\\\y=78,000\times (0.03)^x[/tex]
3.The Expression is
[tex]m^2-13 m -30\\\\a=1, b= -13,c= -30\\\\ac=-30\\\\b=-13= -15 +2,as -15 \times 2 = -30\\\\\text{Equivalent expression}=(m-15)(m+2)[/tex]
Option A: (m-15)(m+2)
[tex]4.\rightarrow x^n=(x^3) \times (x^{-17})\\\\=\text{using law of indices},x^a\times x^b=x^{a+b}\\\\x^n=x^{3-17}\\\\x^n=x^{-14}\\\\n=-14[/tex]
