Solve (1/60) Raised to Negative Fourth Power: Fraction Exponent Challenge

Question

Insert the corresponding expression:

$\left(\frac{1}{60}\right)^{-4}=$

00:00 Simplify the following problem

00:03 According to the exponent laws, a fraction raised to the power (-N)

00:07 equals the reciprocal fraction raised to the opposite power (N)

00:13 We'll apply this formula to our exercise

00:17 Let's invert the fraction

00:21 and proceed to raise it to the opposite power (times(-1))

00:26 This is the solution

To solve for $\left(\frac{1}{60}\right)^{-4}$ , we apply the rule for negative exponents.

Step 1: Use the negative exponent rule: For any non-zero number $a$ , $a^{-n} = \frac{1}{a^n}$ . Thus,

$\left(\frac{1}{60}\right)^{-4} = \left(\frac{60}{1}\right)^4$ .

Step 2: Simplify $\left(\frac{60}{1}\right)^4$ by recognizing the identity $\frac{60}{1} = 60$ , so it follows that:

$\left(\frac{60}{1}\right)^4 = 60^4$ .

Therefore, the simplified expression is $60^4$ .

The correct answer is $60^4$

$60^4$