Respuesta :

Answer:

1/10² = 10⁻²

Step-by-step explanation:

Option 1 : (2⁵)⁵

  • Rule is when a power applied to a term of an existing power, they are multiplied
  • Therefore, (2⁵)⁵ = 2²⁵
  • 2²⁵ ≠ 2¹⁰ ⇒ False

Option 2 : 1/10²

  • A power in the denominator becomes negative when brought to the numerator
  • ⇒ 1/10² = 10⁻²
  • 10⁻² = 10⁻² ⇒ True

Option 3 : 1⁰

  • Any number raised to the power 0 is equal to 1
  • 1⁰ = 1
  • 1 ≠ 0 ⇒ False
ᴜᴋɪʏᴏ

Answer:

[tex]\huge\boxed{\bf\:\frac{1}{10^{2}} = 10^{-2}}[/tex]

Step-by-step explanation:

Let's check all the equations.

[tex]\rule{150pt}{2pt}[/tex]

[tex]1^{0} = 0[/tex]

We know that, any number with 0 as its exponent will be equal to 1. Hence, this equation is incorrect.

[tex]\rule{150pt}{2pt}[/tex]

[tex](2^{5})^{5} = 2^{10}[/tex]

Let's solve the left hand side of the equation first.

[tex](2^{5})^{5}\\= 2^{5\times5}\\= 2^{25}[/tex]

We can see from this that,

[tex]2^{25} \neq 2^{10}[/tex]

Since, the left hand side [tex]\neq[/tex] right hand side, this equation is also false.

[tex]\rule{150pt}{2pt}[/tex]

[tex]\frac{1}{10^{2}} = 10^{-2}[/tex]

According to the identity ⟶ [tex]\bf\:\frac{1}{x^{y}} = x^{-y}[/tex], we can infer that the given equation is correct.

[tex]\rule{150pt}{2pt}[/tex]

So, the correct equation is [tex]\boxed{\bf\:\frac{1}{10^{2}} = 10^{-2}}[/tex].

[tex]\rule{150pt}{2pt}[/tex]

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