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((a^(7))/(a^(-3)))^(0)*(a^(3)(a^(-2))^(4))/(a^(7))
The given expression simplifies to
a^(x), for some integer
x. What is the value of
x ?
Choose 1 answer:
(A) -12
(B) 0
(C) 2
(D) 12

$\left(\frac{a^{7}}{a^{-3}}\right)^{0} \cdot \frac{a^{3}\left(a^{-2}\right)^{4}}{a^{7}}$ $\newline$ The given expression simplifies to $a^{x}$ , for some integer $x$ . What is the value of $x$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-12$ $\newline$ (B) $0$ $\newline$ (C) $2$ $\newline$ (D) $12$

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Compare linear and exponential growth

Full solution

Q.

\left(\frac{a^{7}}{a^{-3}}\right)^{0} \cdot \frac{a^{3}\left(a^{-2}\right)^{4}}{a^{7}}

\newline

The given expression simplifies to

a^{x}

, for some integer

x

. What is the value of

x

?

\newline

Choose

1

answer:

\newline

(A)

-12

\newline

(B)

0

\newline

(C)

2

\newline

(D)

12

Step $1$ : Simplify the expression: First, let's simplify the expression step by step. We start with the first part of the expression: $\left(\frac{a^{7}}{a^{-3}}\right)^{0}$ . Any number (except $0$ ) raised to the power of $0$ is $1$ . So this part of the expression simplifies to $1$ .
Step $2$ : Simplify the exponent in parentheses: Next, we look at the second part of the expression: $(a^{3}(a^{-2})^{4})/(a^{7})$ . We can simplify the exponent in the parentheses first: $(a^{-2})^4 = a^{-2*4} = a^{-8}$ .
Step $3$ : Multiply numbers with the same base: Now we have $a^{3} \times a^{-8}$ in the numerator. When we multiply numbers with the same base, we add the exponents: $a^{3} \times a^{-8} = a^{3 + (-8)} = a^{-5}$ .
Step $4$ : Ignore the $1$ : We now have the expression $1 \times (a^{-5})/(a^{7})$ . Since $1$ multiplied by anything is itself, we can ignore the $1$ . So we are left with $(a^{-5})/(a^{7})$ .
Step $5$ : Divide numbers with the same base: When we divide numbers with the same base, we subtract the exponents: $a^{-5} / a^{7} = a^{-5 - 7} = a^{-12}$ .
Step $6$ : Simplify the expression: The expression simplifies to $a^{-12}$ . Therefore, the value of $x$ is $-12$ , which corresponds to answer choice (A).

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\newline

\newline

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\newline

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f(x)

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\newline

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\newline

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\newline

Simplify any fractions.

\newline

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are differentiable.

\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

Simplify any fractions.

\newline

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\newline

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\newline

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\newline

Simplify any fractions.

\newline

o'(7)=

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