Question

Simplify $\left(\frac{1}{3}\right)^{-3} + \left(\frac{1}{5}\right)^{-4} + \left(\frac{1}{15}\right)^{-2}$.

• A. 856
• B. 756
• C. 877
• D. 777

Answer 1

Answer:

C. 877

The simplified value of the given expression is 877.

$\left(\frac{1}{3}\right)^{-3} + \left(\frac{1}{5}\right)^{-4} + \left(\frac{1}{15}\right)^{-2}$

1. Apply the negative exponent rule $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$:

   • $\left(\frac{1}{3}\right)^{-3} = 3^3$

   • $\left(\frac{1}{5}\right)^{-4} = 5^4$

   • $\left(\frac{1}{15}\right)^{-2} = 15^2$

2. Calculate the value of each term:

   • $3^3 = 3 \times 3 \times 3 = 27$

   • $5^4 = 5 \times 5 \times 5 \times 5 = 625$

   • $15^2 = 15 \times 15 = 225$

3. Add the values together:
   $27 + 625 + 225 = \mathbf{877}$