Choose all the expressions that are equivalent to 458

Question

HINT: solve each and see which one would equal the above expression

45−−√8
8th root of 4 to the 5th power

(2148)(4−14)
open paren 2 raised to the 14 eighths power close paren times open paren 4 raised to the negative 1 fourth power close paren

(478)(4−14)
open paren 4 raised to the 7 eighths power close paren times open paren 4 raised to the negative 1 fourth power close paren

410−−−√5
5th root of 4 to the 10th power

4(438)

Answer 1

Let's evaluate each expression to determine which ones are equivalent to 458.

1. \( \sqrt{45} \cdot 8 \)
   Calculate \( \sqrt{45} = 3\sqrt{5} \), so \( \sqrt{45} \cdot 8 = 3\sqrt{5} \cdot 8 = 24\sqrt{5} \). This does not equal 458.

2. 8th root of \( 4^5 \)
   This can be written as \( (4^5)^{1/8} = 4^{5/8} \). Clearly not equal to 458.

3. \( (2^{148})(4^{-14}) \)
   Rewrite \( 4^{-14} \) as \( (2^2)^{-14} = 2^{-28} \). Thus, \( (2^{148})(4^{-14}) = 2^{148} \cdot 2^{-28} = 2^{148 - 28} = 2^{120} \). This does not equal 458.

4. \( (4^{7/8})(4^{-1/4}) \)
   This simplifies to \( 4^{7/8 - 1/4} = 4^{7/8 - 2/8} = 4^{5/8} \). This does not equal 458.

5. \( 4 \cdot (4^{38}) \)
   This can be rewritten as \( 4^{1} \cdot 4^{38} = 4^{39} \). This value is clearly not equal to 458.

Based on evaluating all expressions above, none of them is equivalent to 458. If there are any misunderstandings about the way to interpret the expressions or if there's a different set of expressions in question, please clarify!