Question

Without evaluating determine weather 2^5 or 4^2 is grater explain

Answer 1

2⁵ is greater than 4²

Explanation:

To determine whether 2⁵ or 4² is greater, we can use the power of a power rule of exponents:

`\boxed{\begin{array}{c}\underline{\textsf{Power of a power rule}}\\\\\left(a^m\right)^n=a^(mn)\end{array}}`

Begin by rewriting 4 as 2²:

`4^2=\left(2^2)^2`

Now, apply the power of a power exponent rule:

`\left(2^2\right)^2=2^(2 \cdot 2)=2^4`

Now that both numbers share the same base of 2, we can compare them without evaluating by analyzing their exponents.

As the exponent of 2⁵ is greater than the exponent of 2⁴, then 2⁵ is greater than 2⁴:

`\Large\boxed{\boxed{\sf 2^5 > 4^2}}`

Answer 2

2^5 is greater than 4^2.

Explanation:

To determine which is greater, 2^5 or 4^2, we can use the following steps:

Break down the powers into their base and exponent forms.

2^5 = (2)(2)(2)(2)(2)

4^2 = (4)(4)

Rewrite 4 as 2^2.

4^2 = (2^2)(2^2) = (2)(2)(2)(2)

Compare the exponents.

2^5 has an exponent of 5, while 4^2 has an exponent of 4.

Therefore, 2^5 is greater than 4^2.