Question

exponent rules - definitions
simplify each expression. find the simplified form in the answer bank. when you find a match, place the question number next to the color. color the picture accordingly to reveal the mystery picture!

1. ( x^5 cdot x^3 )
2. ( x^0 )
3. ( (x^3)^5 )
4. ( \frac{x^{12}}{x^2} )
5. ( x cdot x^5 )
6. ( (xy)^5 )
7. ( x^{-6} )
8. ( x^7 cdot x^2 )
9. ( (x^7)^2 )
10. ( \frac{x^7}{x^2} )
11. ( x^{-1} )
12. ( x cdot x^2 cdot x^3 cdot x^5 )

Explanation:

Step1: Apply product rule ($x^a \cdot x^b = x^{a+b}$)

$x^5 \cdot x^3 = x^{5+3} = x^8$

Step2: Apply zero exponent rule ($x^0=1, x

eq0$)
$x^0 = 1$

Step3: Apply power rule ($(x^a)^b = x^{a \cdot b}$)

$(x^3)^5 = x^{3 \cdot 5} = x^{15}$

Step4: Apply quotient rule ($\frac{x^a}{x^b}=x^{a-b}$)

$\frac{x^{12}}{x^2} = x^{12-2} = x^{10}$

Step5: Apply product rule ($x=x^1$)

$x \cdot x^5 = x^{1+5} = x^6$

Step6: Apply product power rule ($(xy)^a=x^a y^a$)

$(xy)^5 = x^5 y^5$

Step7: Apply negative exponent rule ($x^{-a}=\frac{1}{x^a}$)

$x^{-6} = \frac{1}{x^6}$

Step8: Apply product rule

$x^7 \cdot x^2 = x^{7+2} = x^9$

Step9: Apply power rule

$(x^7)^2 = x^{7 \cdot 2} = x^{14}$

Step10: Apply quotient rule

$\frac{x^7}{x^2} = x^{7-2} = x^5$

Step11: Apply negative exponent rule

$x^{-1} = \frac{1}{x}$

Step12: Apply product rule ($x=x^1$)

$x \cdot x^2 \cdot x^3 \cdot x^5 = x^{1+2+3+5} = x^{11}$

Answer:

1. $x^8$
2. $1$
3. $x^{15}$
4. $x^{10}$
5. $x^6$
6. $x^5 y^5$
7. $\frac{1}{x^6}$
8. $x^9$
9. $x^{14}$
10. $x^5$
11. $\frac{1}{x}$
12. $x^{11}$