Question

Math

Posted 3 months ago

```
Select the equivalent expression.
$\left(3^{-8} \cdot 7^{3}\right)^{-2}=?$
Choose 1 answer:
(A) $21^{10}$
(B) $\frac{7^{6}}{3^{16}}$
(c) $3^{16} \cdot 7^{-6}$
```

Sign in to unlock the answer

Answer from Sia

Posted 3 months ago

Solution by Steps

step 2

We apply the power of a product rule, which states that $(ab)^n = a^n \cdot b^n$, to get $\left(3^{-8}\right)^{-2} \cdot \left(7^{3}\right)^{-2}$

step 3

Next, we apply the power of a power rule, which states that $(a^m)^n = a^{mn}$, to simplify the expression to $3^{16} \cdot 7^{-6}$

step 4

The simplified expression is $3^{16} \cdot 7^{-6}$, which matches one of the answer choices

C

Key Concept

Exponent Rules

Explanation

When simplifying expressions with exponents, we use the power of a product rule and the power of a power rule to find the equivalent expression.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question