CPM Homework Help : MC2 Problem 10-98

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10-98.

Expand and simplify each expression, or use the exponent patterns you identified in Section 10.1 to simplify.

Hint:

Refer to the Math Notes box in Lesson 10.1.6 to review the Laws of Exponents.

$\frac { x ^ { 4 } } { x ^ { 3 } }$
Hint (a):
When dividing like variables, subtract the exponent in the denominator from the exponent in the numerator.
Help (a):
$x^{(4-3)}$

$(x^3)^4$
Hint (b):
When there is an exponent outside of the parentheses, multiply the exponent with the exponent of every variable inside the parentheses.
Help (b):
$x^{(4-3)}$

$(2y^2)^2$
Help (c):
$2^2 y^{(2)(2)}$

$(x^2)^4$
Help (d):
See part (b).

$x^2x^{–3}$
Help (e):
Use the rule $(x^a)(x^b) = x^{(a+b)}$ .
Answer (e):
$x^{-1}$

$(xy^2)^2$
Help (f):
See part (c).
Answer (f):
$x^2y^4$

$(x^2y^2)^4$
Help (g):
See part (c).

$(2x)^3$
Help (h):
See part (c).
Answer (h):
$8x^3$

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