Exponent Rules or Laws — Steemit - Free Printable

Let's solve each of the exponential problems step by step using the laws of exponents.

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Problem 1: $ 2^3 \times 2^2 $

Step-by-step:

We use the product of powers rule:
> $ a^m \times a^n = a^{m+n} $

So:
$$
2^3 \times 2^2 = 2^{3+2} = 2^5
$$

✔ Answer: $ 2^5 $

> *(As shown in the hint, $ 2^3 = 2 \times 2 \times 2 $, $ 2^2 = 2 \times 2 $, so total is five 2s multiplied → $ 2^5 $)*

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Problem 2: $ 5 \times 5^4 \times 5^3 $

First, note that the first term is just $ 5 $, which can be written as $ 5^1 $.
Now apply the product of powers rule:

$$
5^1 \times 5^4 \times 5^3 = 5^{1+4+3} = 5^8
$$

✔ Answer: $ 5^8 $

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Problem 3: $ (3abc)^0 $

Use the zero exponent rule:
> Any non-zero number raised to the power of 0 is 1.

So:
$$
(3abc)^0 = 1
$$

✔ Answer: $ 1 $

> *Note: As long as $ 3abc \neq 0 $, this holds true.*

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Problem 4: $ \frac{4^4}{4^2} $

Use the quotient of powers rule:
> $ \frac{a^m}{a^n} = a^{m-n} $

$$
\frac{4^4}{4^2} = 4^{4-2} = 4^2
$$

Now compute $ 4^2 = 16 $

✔ Answer: $ 16 $ or $ 4^2 $ (both acceptable, but simplified value is $ 16 $)

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Problem 5: $ (5^4)^2 $

Use the power of a power rule:
> $ (a^m)^n = a^{m \times n} $

$$
(5^4)^2 = 5^{4 \times 2} = 5^8
$$

✔ Answer: $ 5^8 $

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✔ Final Answers:

1. $ 2^5 $
2. $ 5^8 $
3. $ 1 $
4. $ 16 $
5. $ 5^8 $

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Let me know if you'd like these explained with more examples!