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Oksanka [162]
2 years ago
11

Which could be the first step in simplifying this expression? Check all that apply. (x cubed x Superscript negative 6 Baseline)

squared (x Superscript negative 18 Baseline) squared (x Superscript negative 3 Baseline) squared (x Superscript negative 2 Baseline) squared x Superscript 6 Baseline x Superscript negative 12 Baseline x Superscript 5 Baseline x Superscript negative 4. Need Help ASAP!

Mathematics
1 answer:
PtichkaEL [24]2 years ago
8 0

Answer:

(x^{-3} )^{2}

x^6 x^{-12}

Step-by-step explanation:

(x^{3} x^{-6} )^{2} is the expression given to be solved.

First of all let us have a look at <u>3 formulas</u>:

1.\ p^a \times p^b = p^{(a+b)}\\2.\ (p^a \times q^b)^c = (p^{a})^c \times (q^{b})^c\\3.\ (p^a)^b = p^{a\times b}

Both the formula can be applied to the expression((x^{3} x^{-6} )^{2}) during the first step while solving it.

<u>Applying formula (1):</u>

(x^{3} x^{-6} )^{2}

Comparing the terms of (x^{3} x^{-6} ) with p^a \times p^b

p=x, a =3, b=-6

\Rightarrow x^{3+(-6)}\\\Rightarrow x^{3-6}\\\Rightarrow x^{-3}

So, (x^{3} x^{-6} )^{2} is reduced to (x^{-3} )^{2}

<u>Applying formula (2):</u>

Comparing the terms of (x^{3} x^{-6} )^{2} with (p^a \times q^b)^c

p=q=x, a =3, b=-6, c=2

\Rightarrow (x^{3})^2\times (x^{-6})^2\\\text{Applying Formula (3)}\\x^6 x^{-12}

So, (x^{3} x^{-6} )^{2} is reduced to x^6 x^{-12}.

So, the answers can be:

(x^{-3} )^{2}

x^6 x^{-12}

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