Question

which expression(s) are equivalent to ( x^{18} ) (mark all that apply)
( \frac{x^{20}}{x^2} )
( x^3x^6 )
( \frac{x^{20}}{x^2} )
( (x^3)^6 )
( x^7x^{11} )
( \frac{x^{18}}{x} )
( x^9x^2 )
28 multiple choice 1 point
suppose ( f(x) = 9x - 7 ) and ( g(x) = -3x + 8 ). find the value of ( \frac{g(0)}{f(3)} )
( -\frac{5}{2} )
( -\frac{2}{5} )
( \frac{2}{5} )
( \frac{5}{2} )
0
-7
7

Explanation:

First Problem (Equivalent to $x^{18}$)

Step1: Simplify $\frac{x^{26}}{x^2}$

Use exponent rule $\frac{x^a}{x^b}=x^{a-b}$:
$x^{26-2}=x^{24}$

Step2: Simplify $x^3x^6$

Use exponent rule $x^a x^b=x^{a+b}$:
$x^{3+6}=x^9$

Step3: Simplify $\frac{x^{20}}{x^3}$

Use exponent rule $\frac{x^a}{x^b}=x^{a-b}$:
$x^{20-3}=x^{17}$

Step4: Simplify $(x^3)^6$

Use exponent rule $(x^a)^b=x^{a \cdot b}$:
$x^{3 \cdot 6}=x^{18}$

Step5: Simplify $x^7x^{11}$

Use exponent rule $x^a x^b=x^{a+b}$:
$x^{7+11}=x^{18}$

Step6: Simplify $\frac{x^{18}}{x}$

Use exponent rule $\frac{x^a}{x^b}=x^{a-b}$:
$x^{18-1}=x^{17}$

Step7: Simplify $x^9x^2$

Use exponent rule $x^a x^b=x^{a+b}$:
$x^{9+2}=x^{11}$

Step1: Calculate $g(0)$

Substitute $x=0$ into $g(x)=-3x+8$:
$g(0)=-3(0)+8=8$

Step2: Calculate $f(3)$

Substitute $x=3$ into $f(x)=9x-7$:
$f(3)=9(3)-7=27-7=20$

Step3: Compute $\frac{g(0)}{f(3)}$

$\frac{8}{20}=\frac{2}{5}$

Answer:

$(x^3)^6$, $x^7x^{11}$

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Second Problem ($\frac{g(0)}{f(3)}$)