Simplify the Fraction Expression: 8/8⁴ Step-by-Step

Video Solution

Solution Steps

00:00 Simply

00:02 every number is actually to the power of 1

00:05 We will use this formula in our exercise, and raise to the power of 1

00:08 According to the laws of exponents, division of exponents with equal bases (A)

00:11 equals the same base (A) to the power of the difference of exponents (M-N)

00:14 We will use this formula in our exercise

00:17 We'll keep the base, and subtract between the exponents

00:20 According to the laws of exponents, any base (A) to the power of (-N)

00:23 equals the reciprocal number (1/A) to the opposite power (N)

00:26 We will use this formula in our exercise

00:28 And this is the solution to the question

Step-by-Step Solution

To solve the expression $\frac{8}{8^4}$ , we will simplify it using the exponent rule for dividing powers with the same base:

Step 1: Identify the expression as $\frac{8^1}{8^4}$ . Both terms have base 8.
Step 2: Apply the formula $\frac{a^m}{a^n} = a^{m-n}$ . Here, $m = 1$ and $n = 4$ .
Step 3: Perform the subtraction in the exponent: $8^{1-4}$ .

Now, calculating the exponent:

$8^{1-4} = 8^{-3}$ .

We know that a negative exponent indicates the reciprocal, so:

$8^{-3} = \frac{1}{8^3}$ .

Thus, the simplified expression is $\frac{1}{8^3}$ .

Based on the choices given, the correct option is:

$\frac{1}{8^3}$ (Choice 1): This matches our simplified expression.
$8^3$ (Choice 2): Incorrect, as it does not simplify the division.
$8^{-4}$ (Choice 3): Incorrect, because it incorrectly represents the situation.
$8^4$ (Choice 4): Incorrect, as it doesn't simplify the expression.

Therefore, the solution to the problem is: $\frac{1}{8^3}$ .

I am confident in the correctness of this solution.