Express 1/6^7: Converting a Fraction to Negative Exponent Form

Question

Insert the corresponding expression:

$\frac{1}{6^7}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, a number raised to the power of (-N)

00:08 is equal to the reciprocal number raised to the opposite power (N)

00:10 We will apply this formula to our exercise

00:13 We'll convert to the reciprocal number, and raise it to the opposite power (times(-1))

00:19 This is the solution

Step-by-Step Solution

To solve this problem, we will rewrite the expression $\frac{1}{6^7}$ using the rules of exponents:

Step 1: Identify the given fraction.

We start with $\frac{1}{6^7}$ , where the base in the denominator is 6, and the exponent is 7.

Step 2: Apply the formula for negative exponents.

The formula $a^{-n} = \frac{1}{a^n}$ allows us to rewrite a reciprocal power as a negative exponent. This means the expression $\frac{1}{6^7}$ can be rewritten as $6^{-7}$ .

Step 3: Conclude with the answer.

By transforming $\frac{1}{6^7}$ to its equivalent form using negative exponents, the expression becomes $6^{-7}$ .

Therefore, the correct expression is $\boxed{6^{-7}}$ , which corresponds to choice 2 in the given options.

Answer

$6^{-7}$

Related Subjects

Question Types

Powers of a Fraction: Inverse formula Powers of a Fraction: Presenting powers in the denominator as powers with negative exponents Negative Exponents: Presenting powers in the denominator as powers with negative exponents