Answer: 2^60 = 8^20
Step-by-step explanation: 8=2^3
(2^3)^20 Multiply the exponents
2⁶⁰ written as an exponent with a base of 8 is 8²⁰
From the question,
The given expression is 2^60
In order to write this as an exponent with a base of 8,
First, let us write the given exponent properly.
The given exponent can be properly written as 2⁶⁰
Now, to write this as an exponent with a base of 8, we will apply one of the laws of indices
From one of the laws of indices, we have that
xᵃᵇ = (xᵃ)ᵇ
Then,
2⁶⁰ can be expressed as 2³⁽²⁰⁾
That is,
2⁶⁰ = (2³)²⁰
But, 2³ = 8
∴ 2⁶⁰ = (2³)²⁰ = 8²⁰
2⁶⁰ = 8²⁰
Hence, 2⁶⁰ written as an exponent with a base of 8 is 8²⁰
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