Question

8^3 * 16^6 * 32^4 = ?
(Use 2 as the base)

Answer 1

`8^3\cdot 16^6\cdot 32^4\qquad \begin{cases} 8=2^3\\ 16=2^4\\ 32=2^5 \end{cases}\implies (2^3)^3\cdot (2^4)^6\cdot (2^5)^4 \\\\\\ 2^((3)(3))\cdot 2^((4)(6))\cdot 2^((5)(4))\implies 2^9\cdot 2^(24)\cdot 2^(20)\implies 2^(9+24+20)\implies {\Large \begin{array}{llll} 2^(53) \end{array}}`

Answer 2

`8^3 \cdot 16^6 \cdot 32^4=2^(53)`

Explanation:

Given expression:

`8^3 \cdot 16^6 \cdot 32^4`

Rewrite:

• 8 = 2 · 2 · 2 = 2³
• 16 = 2 · 2 · 2 · 2 = 2⁴
• 32 = 2 · 2 · 2 · 2 · 2 = 2⁵

`\implies (2^3)^3 \cdot (2^4)^6 \cdot (2^5)^4`

`\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):`

`\implies 2^(3 * 3) \cdot 2^(4 * 6) \cdot 2^(5 * 4)`

`\implies 2^(9) \cdot 2^(24) \cdot 2^(20)`

`\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c):`

`\implies 2^(9+24+20)`

`\implies 2^(53)`