Solve 7⁴ × 8³ × (1/7)⁴: Power and Reciprocal Multiplication

Question

$7^4\cdot8^3\cdot(\frac{1}{7})^4=\text{?}$

00:09 Let's simplify the problem together.

00:15 If a fraction has an exponent, both the top and bottom numbers are raised to that power.

00:24 We'll use this rule for our exercise, so let's get started!

00:30 Now, let's reduce wherever we can.

00:38 Remember, one raised to any power is always one.

00:44 And there you go, that's the solution!

We use the formula:

$(\frac{a}{b})^n=\frac{a^n}{b^n}$

We decompose the fraction inside of the parentheses:

$(\frac{1}{7})^4=\frac{1^4}{7^4}$

We obtain:

$7^4\times8^3\times\frac{1^4}{7^4}$

We simplify the powers: $7^4$

We obtain:

$8^3\times1^4$

Remember that the number 1 in any power is equal to 1, thus we obtain:

$8^3\times1=8^3$

$8^3$