CPM Homework Help : CC3MN Problem 9-64

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9-64.

Simplify each of the following expressions.

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

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

$m^2n · 9mn$
Hint (c):
See part (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 with the lowest base numbers possible
$\frac{(3^{5})(2^{3})(5^{3})}{(3^{2})(2^{3})(5^{3})(3^{3})}$
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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