Math Problem Statement

Laipsnį pakeiskite laipsniu, kurio pagrindas 2:

Solution

The problem asks to express the given numbers as powers of 2. Let's go through each part:

a) 424^2:

  • 4=224 = 2^2, so 42=(22)2=244^2 = (2^2)^2 = 2^{4}.

b) 1283128^3:

  • 128=27128 = 2^7, so 1283=(27)3=221128^3 = (2^7)^3 = 2^{21}.

c) 2562256^2:

  • 256=28256 = 2^8, so 2562=(28)2=216256^2 = (2^8)^2 = 2^{16}.

d) 828^2:

  • 8=238 = 2^3, so 82=(23)2=268^2 = (2^3)^2 = 2^6.

e) 434^3:

  • 4=224 = 2^2, so 43=(22)3=264^3 = (2^2)^3 = 2^6.

f) 5124512^4:

  • 512=29512 = 2^9, so 5124=(29)4=236512^4 = (2^9)^4 = 2^{36}.

g) 32332^3:

  • 32=2532 = 2^5, so 323=(25)3=21532^3 = (2^5)^3 = 2^{15}.

h) 64264^2:

  • 64=2664 = 2^6, so 642=(26)2=21264^2 = (2^6)^2 = 2^{12}.

i) 1284128^4:

  • 128=27128 = 2^7, so 1284=(27)4=228128^4 = (2^7)^4 = 2^{28}.

j) 2564256^4:

  • 256=28256 = 2^8, so 2564=(28)4=232256^4 = (2^8)^4 = 2^{32}.

k) 16516^5:

  • 16=2416 = 2^4, so 165=(24)5=22016^5 = (2^4)^5 = 2^{20}.

l) 102451024^5:

  • 1024=2101024 = 2^{10}, so 10245=(210)5=2501024^5 = (2^{10})^5 = 2^{50}.

Each expression has been rewritten with a base of 2.

Would you like more details on any of these steps?

Here are five related questions for further practice:

  1. How do you express 64364^3 as a power of 2?
  2. Simplify 5125512^5 as a power of 2.
  3. Convert 16416^4 into a power of 2.
  4. Express 102431024^3 with a base of 2.
  5. How can you rewrite 444^4 as a power of 2?

Tip: When expressing numbers as powers of 2, start by finding how the base can be written as 2k2^k, and then use exponent rules to simplify.

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Math Problem Analysis

Mathematical Concepts

Exponents
Powers of Two

Formulas

a^m = (b^n)^m = b^(n*m)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 9-11