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: Add exponents (product rule)

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

Step2: Apply zero exponent rule

$x^0 = 1$ (for $x
eq 0$)

Step3: Multiply exponents (power rule)

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

Step4: Subtract exponents (quotient rule)

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

Step5: Add exponents (product rule)

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

Step6: Distribute exponent (product power rule)

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

Step7: Rewrite negative exponent

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

Step8: Add exponents (product rule)

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

Step9: Multiply exponents (power rule)

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

Step10: Subtract exponents (quotient rule)

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

Step11: Rewrite negative exponent

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

Step12: Add exponents (product rule)

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

Answer:

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