Question

Find the value of the following expression

(2^8 5^-5 19^0) x [5^-2 over 2^3]^4 x 2^28 (5 points)

Write your answer in simplified form. Show all of your steps. (5 points)

Answer 1

Looks like the expression is

(2⁸ • 5⁻⁵ • 19⁰) • (5⁻² / 2³)⁴ • 2²⁸

First, any positive number raised to 0 is 1:

(2⁸ • 5⁻⁵ • 1) • (5⁻² / 2³)⁴ • 2²⁸

(2⁸ • 5⁻⁵) • (5⁻² / 2³)⁴ • 2²⁸

Exponents in a denominator can be rewritten as negative exponents in the numerator:

(2⁸ • 5⁻⁵) • (5⁻² • 2⁻³)⁴ • 2²⁸

Distribute the 4th power across the product 5⁻² • 2⁻³ :

(5⁻² • 2⁻³)⁴ = 5⁻⁸ • 2⁻¹²

so we have

(2⁸ • 5⁻⁵) • (5⁻⁸ • 2⁻¹²) • 2²⁸

Multiplication is associative, so we can ignore the parentheses. Combine factors with equal bases and simplify the exponents:

2⁸ • 5⁻⁵ • 5⁻⁸ • 2⁻¹² • 2²⁸

2⁸⁻¹²⁺²⁸ • 5⁻⁵⁻⁸

2²⁴ • 5⁻¹³

Rewrite the negative exponent as a positive one:

2²⁴ / 5¹³