Math / Numbers & Operations

Question32 $\left(2^{3}\right)^{2}=$ 64

Studdy Solution

STEP 1

What is this asking? We need to calculate what $(2^3)^2$ is! Watch out! Don't multiply the exponents directly.
Remember the power of a power rule!

STEP 2

1. Expand the expression
2. Multiply the exponents
3. Calculate the result

STEP 3

Alright, let's break down this seemingly scary expression!
We have $(2^3)^2$ .
This tells us we have $2^3$ multiplied by itself two times.
It's like having a power packed with another power!

STEP 4

So, we can rewrite this as: $(2^3)^2 = (2^3) \cdot (2^3)$ See? Not so intimidating anymore!

STEP 5

Now, remember our exponent rules!
When we multiply numbers with the same base, we add the exponents.
Here, our base is $2$ , and our exponents are both $3$ .

STEP 6

Let's apply this rule: $(2^3) \cdot (2^3) = 2^{3+3}$

STEP 7

Adding the exponents gives us: $2^{3+3} = 2^6$ Boom! We've simplified our expression significantly.

STEP 8

Now, we just need to figure out what $2^6$ is.
This means multiplying $2$ by itself six times.

STEP 9

Let's calculate: $2^6 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$

STEP 10

We can break this down for easier calculation: $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = (2 \cdot 2) \cdot (2 \cdot 2) \cdot (2 \cdot 2) = 4 \cdot 4 \cdot 4 = 16 \cdot 4 = 64$

STEP 11

So, our final result is $64$ !

STEP 12

$(2^3)^2 = 64$

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