Question

The expression (x^3)(x^-17) is equivalent to x^n. what is the value of n record your answer and fill in the bubbles on the answer document
Can anybody answer all the questions

Answer 1

Answer with explanation:

1.→Answer Written by Jack is Incorrect.

$m^n=\text{exponent}\\\\\frac{x^a}{x^b}=x^{a-b}\\\\x^a \times x^b=x^{a+b}$

Error:Instead of subtracting powers,jack has added powers of same exponent.

Correct Solution:

    $=\frac{54\times x^9 \times y^8}{6\times x^3 \times y^4}\\\\ \text{Here ,correct answer should be}=9\times x^{9-3} \times y^{8-4}\\\\=9 x^6 y^4$

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

  $y=a\times b^x\\\\y=78,000\times (0.03)^x$

3.The Expression is

$m^2-13 m -30\\\\a=1, b= -13,c= -30\\\\ac=-30\\\\b=-13= -15 +2,as -15 \times 2 = -30\\\\\text{Equivalent expression}=(m-15)(m+2)$

Option A: (m-15)(m+2)  

$4.\rightarrow x^n=(x^3) \times (x^{-17})\\\\=\text{using law of indices},x^a\times x^b=x^{a+b}\\\\x^n=x^{3-17}\\\\x^n=x^{-14}\\\\n=-14$  

Answer 2

Exercise 1:

The exponents are wrong: when you divide two power, you subtract the exponents:

$\dfrac{54x^9y^8}{6x^3y^4} = \dfrac{54}{6}x^{9-3}y^{8-4} = 9x^6y^4$

Exercise 2:

The function represents a growth rate of 300%! 3% is actually written as 0.03, so the correct function is

$78000\cdot 0.03^x$

Exercise 3:

To factor a quadratic equation, we have to find the roots. Once you have the roots $m_1, m_2$, you can factor the expression as $(m-m_1)(m-m_2)$

In this case, the solutions are $m=-2,\ m=15$, which yields the factorization

$(m+2)(m-15)$

Exercise 4:

When you multiply two powers of the same base, you add the exponents:

$a^b\cdot a^c = a^{b+c}$

So, in your case, you have

$x^{3}\cdot x^{-17} = x^{3-17} = x^{-14}$