Question

Select all of the expressions that are equivalent to 2.5¹⁶

2.5⁴ ⋅ 2.5⁴

1.25¹⁶ ⋅ 2¹⁶

2.5⁸ ⋅ 2.5⁸

(2.5⁸)⁸

(2.5⁸)²

Answer 1

• 1.25¹⁶ ⋅ 2¹⁶
• 2.5⁸ ⋅ 2.5⁸
• (2.5⁸)²

Explanation:

You have a number of expressions involving exponents, and you want those equivalent to 2.5¹⁶.

Rules of exponents

The relevant rules of exponents are ...

(a^b)(a^c) = a^(b+c)

(a^b)^c = a^(bc)

(ab)^c = (a^c)(b^c)

Given expressions

Then the simplified form of the given expressions will be ...

2.5⁴ ⋅ 2.5⁴ = 2.5⁸ . . . . exponents are added

1.25¹⁶ ⋅ 2¹⁶ = (1.25 · 2)¹⁶ = 2.5¹⁶ . . . . exponent is distributed

2.5⁸ ⋅ 2.5⁸ = 2.5¹⁶ . . . . exponents are added

(2.5⁸)⁸ = 2.5⁶⁴ . . . . exponents are multiplied

(2.5⁸)² = 2.5¹⁶ . . . . exponents are multiplied

The equivalent expressions are shown in bold, above.