CPM Homework Help : AC Problem 11-15

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11-15.

Simplify each expression using the laws of exponents.

$\left(x^2\right)\left(x^2y^3\right)$

Hint (a):
How many factors of $x$ are multiplied? How many of $y$ ?
Answer (a):
$\left(x^2\cdot x^2\right)\left(y^3\right)=x^4y^3$

$\frac { x ^ { 3 } y ^ { 4 } } { x ^ { 2 } y ^ { 3 } }$

Hint (b):
Think about making ones and where any left over factors would remain.
Answer (b):
$xy$

$\left(2x^2\right)\left(-3x^4\right)$

Hint (c):
How many factors of $x$ are multiplied?
Multiply the constants separately.
Answer (c):
$\left(x^2\cdot x^4\right)\left(2\cdot-3\right)=-6x^6$

$\left(2x\right)^3$

Hint (d):
Write $2x$ three times and follow the pattern from part (a).

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