Question

1. evaluate the expression: $(3a^{2}b^{4})^{3}$

a) $9a^{5}b^{7}$
b) $27a^{6}b^{12}$
c) $3a^{6}b^{12}$
d) $27a^{5}b^{7}$
a
b
c
d
#4 (hint: the answer is not a!)

1. what is the value of $(15xy^{3}z^{5})^{0}$?

a) 0
b) 15
c) 1
d) $15xyz$
a
b
c
d

Explanation:

Step1: Apply power of a product rule

$(3a^2b^4)^3 = 3^3 \cdot (a^2)^3 \cdot (b^4)^3$

Step2: Calculate each term

$3^3=27$, $(a^2)^3=a^{2\times3}=a^6$, $(b^4)^3=b^{4\times3}=b^{12}$

Step3: Combine the terms

$27 \cdot a^6 \cdot b^{12} = 27a^6b^{12}$
---

Step1: Apply zero exponent rule

Any non-zero term to the power of 0 is 1. Since $15xy^3z^5
eq 0$, $(15xy^3z^5)^0 = 1$

Answer:

1. B) $27a^6b^{12}$
2. C) 1