Question

product of powers property

1. $a^{7}a^{12} = $
2. $c^{3}c^{8}c^{-5} = $
3. $(2d^{7})(-4d^{9}d^{5}) = $
4. $(9x^{10}y^{3})(-x^{5}y^{3}) = $

Explanation:

Step1: Apply product of powers rule

For $a^7a^{12}$, add exponents: $a^{7+12}=a^{19}$

Step2: Apply product of powers rule

For $c^3c^8c^{-5}$, add exponents: $c^{3+8+(-5)}=c^{6}$

Step3: Multiply coefficients, add exponents

For $(2d^7)(-4d^9d^5)$: first multiply coefficients $2\times(-4)=-8$, then add exponents $d^{7+9+5}=d^{21}$, so $-8d^{21}$

Step4: Multiply coefficients, add exponents

For $(9x^{10}y^3)(-x^5y^3)$: multiply coefficients $9\times(-1)=-9$, add $x$ exponents $x^{10+5}=x^{15}$, add $y$ exponents $y^{3+3}=y^6$, so $-9x^{15}y^6$

Answer:

1. $a^{19}$
2. $c^{6}$
3. $-8d^{21}$
4. $-9x^{15}y^6$