CPM Homework Help : PCT Problem 1-26

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1-26.

Simplify using the rules of exponents. Or state why it cannot be simplified.

Hint:

Math Notes

Rules of Exponents

$x^{m} · x^{n} = x^{m + n}$
$( \frac { x ^ { m } } { x ^ { n } } )= x^{m − n}$
$\left(x^{m} \right) ^{n} = x^{mn}$
$\left(xy\right) ^{m} = x^{m}y^{m}$
$( \frac { x } { y } ) ^ { n } = \frac { x ^ { n } } { y ^ { n } }$

Rules 1, 2, and 3 are the most commonly used, but rules 4 and 5 are also useful.

$a^{b} · a^{c}$
Answer (a):
$a^{b+c}$

$a^{−b}· a^{c}$
Answer (b):
$a^{(c-b)}$

$a^{b} + a^{c}$
Answer (c):
Can't be simplified. We are not multiplying.

$a · a^{b}$
Answer (d):
$a^{b+1}$

$a^{0} · a^{b}$
Answer (e):
$a^b$

$a^{(b + c)} · a^{2c}$
Answer (f):
$a^{(3c+b)}$

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