Help me plezzzzzzz im bad at math

Question

asked Sep 21, 2024 214k views

1 Answer

Daughter · Answer 1 · 2024-09-27T22:14:03+0000

Answer:

64

Explanation:

Given expression:

$2^2\cdot2^4\cdot(4^1)/(4^(-1))\cdot2^(-4)\cdot 10^0\cdot 1$

To solve, begin by rearranging the given expression to collect terms with the same bases:

$1\cdot 2^2\cdot2^4\cdot 2^(-4)\cdot(4^1)/(4^(-1))\cdot10^0$

$\textsf{Apply the exponent rule:} \quad a^0=1$

$1\cdot 2^2\cdot2^4\cdot 2^(-4)\cdot(4^1)/(4^(-1))\cdot1$

Apply the rule a · 1 = a:

$2^2\cdot2^4\cdot 2^(-4)\cdot(4^1)/(4^(-1))$

$\textsf{Apply the exponent rule:} \quad (a^b)/(a^c)=a^(b-c)$

$2^2\cdot2^4\cdot 2^(-4)\cdot 4^(1-(-1))$

$2^2\cdot2^4\cdot 2^(-4)\cdot 4^(2)$

Rewrite 4 as 2²:

$2^2\cdot2^4\cdot 2^(-4)\cdot (2^2)^(2)$

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

$2^2\cdot2^4\cdot 2^(-4)\cdot 2^4$

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

2^(2+4-4+4)

2^(6)

Finally, compute 2⁶:

$2^(6)=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2=64$

Therefore, the given expression is equal to:

$\Large\boxed{\boxed{64}}$