Simplify each of the expressions below. $$ \begin{array}{ll} ext { 1. }\left(5^{3} ight)^{3} 39 & 4 . \ \left(3^{4} ight)^{2}\end{array} $$

Question

Simplify each of the expressions below. $$ \begin{array}{ll}	ext { 1. }\left(5^{3}ight)^{3} 39 & 4 . \ \left(3^{4}ight)^{2}\end{array} $$

UpStudy AI · Accepted Answer

We are given two expressions:

1. (5³)³  
2. (3⁴)²

To simplify these expressions, use the exponent rule for powers raised to powers:  
  (a^b)^c = a^(b × c)

Step 1: Simplify each expression using the rule.

For the first expression:  
  (5³)³ = 5^(3 × 3) = 5⁹

For the second expression:  
  (3⁴)² = 3^(4 × 2) = 3⁸

Step 2: (Optional) Compute the numerical values.

For 5⁹:  
5⁹ = 5 × 5 × ... (9 times)  
Calculating, 5⁹ = 1,953,125

For 3⁸:  
3⁸ = 3 × 3 × ... (8 times)  
Calculating, 3⁸ = 6,561

Thus, the simplified forms are:

1. (5³)³ = 5⁹ = 1,953,125  
2. (3⁴)² = 3⁸ = 6,561
$$ (5^3)^3 = 5^9 = 1,953,125 $$ $$ (3^4)^2 = 3^8 = 6,561 $$

Simplify each of the expressions below. \( \begin{array}{ll}\text { 1. }\left(5^{3}\right)^{3} 39 & 4 . \\ \left(3^{4}\right)^{2}\end{array} \)