Which expression is equivalent to $$ \left(7^{-8}\right)\left(7^{3}\right) $$ ? Option 1 $$ 49^{-5} $$ Option 3

Question

UpStudy AI · Accepted Answer

To determine which expression is equivalent to $$ \left(7^{-8}\right)\left(7^{3}\right) $$, we can use the properties of exponents. Specifically, when multiplying expressions with the same base, you add their exponents:

$$
7^{-8} \times 7^{3} = 7^{-8 + 3} = 7^{-5}
$$

So, $$ \left(7^{-8}\right)\left(7^{3}\right) $$ simplifies to $$ 7^{-5} $$, which can also be written as:

$$
\frac{1}{7^{5}}
$$

**Reviewing the Options:**

- **Option 1:** $$ 49^{-5} $$

Since $$ 49 = 7^2 $$, this can be rewritten as:
  
  $$
  (7^2)^{-5} = 7^{-10}
  $$
  
  This is **not** equal to $$ 7^{-5} $$.

- **Option 3:** *(Assuming based on the context)* $$ 7^{-5} $$

This directly matches our simplified expression.

**Conclusion:**

The expression equivalent to $$ \left(7^{-8}\right)\left(7^{3}\right) $$ is:

$$
7^{-5}
$$

Assuming the options provided include this form, **Option 3** is the correct equivalent expression.
The expression equivalent to $$ \left(7^{-8}\right)\left(7^{3}\right) $$ is $$ 7^{-5} $$.

Which expression is equivalent to ?
Option 1

Option 3

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions

Which expression is equivalent to ? Option 1 Option 3