CPM Homework Help : MC2 Problem 11-42

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11-42.

Simplify each of the following expressions.

$4x^3y · 3xy^2$
Hint (a):
Combine like terms.
$\left(4\right)\left(3\right)x^{\left(3 + 1\right)}y^{\left(1 + 2\right)}$
Answer (a):
$12x^4y^3$

$6a^5b^2 · 3ab^2$
Hint (b):
See (a).
Answer (b):
$18a^6b^4$

$m^2n · 9mn$
Hint (c):
See (a).

$\frac { 3 ^ { 5 } \cdot 8 \cdot 5 ^ { 3 } } { 3 ^ { 2 } \cdot 2 ^ { 3 } \cdot 5 ^ { 3 } \cdot 3 ^ { 3 } }$
Step 1(d):
Rewrite this expression.
$\frac{(3^{5})(2^{3})(5^{3})}{(3^{5})(2^{3})(5^{3})(3^{3})}$
Step 2(d):
Combine numbers with the same base.
$(3^{(5 − 2 − 3)}) · (2^{(3 − 3)}) · (5^{(3 − 3)})$
Step 3(d):
$(3^0) · (2^0) · (5^0)$
Hint (d):
Any number to the zero power has the value of $1$ .
Answer (d):
$1$

$\frac { m ^ { 4 } \cdot n } { n ^ { 3 } }$
Hint (e):
See (d).
Answer (e):
$\frac{m^{4}}{n^{2}}$

$\frac { 9 a ^ { 4 } b ^ { 2 } } { 15 b }$
Hint (f):
See (d).

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