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Problem 72

# Simplify (a) $$2^{3} \cdot 2^{2}$$ (b) $$\mathrm{a}^{3} \cdot \mathrm{a}^{5}$$ (c) $$x^{6} \cdot x^{4}$$

Expert verified
(a) $$2^{5}$$ (b) $$a^{8}$$ (c) $$x^{10}$$
See the step by step solution

## Step 1: a) Simplify $$2^{3} \cdot 2^{2}$$

We are multiplying two numbers with the same base (2), so we can apply the product rule of exponents to add the exponents: $$2^{3} \cdot 2^{2} = 2^{3+2}$$. Now, simply add the exponents: $$3+2 = 5$$. Therefore, the simplified expression is: $$2^{5}$$.

## Step 2: b) Simplify $$a^{3} \cdot a^{5}$$

We are multiplying two numbers with the same base (a), so we can apply the product rule of exponents to add the exponents: $$a^{3} \cdot a^{5} = a^{3+5}$$. Now, simply add the exponents: $$3+5 = 8$$. Therefore, the simplified expression is: $$a^{8}$$.

## Step 3: c) Simplify $$x^{6} \cdot x^{4}$$

We are multiplying two numbers with the same base (x), so we can apply the product rule of exponents to add the exponents: $$x^{6} \cdot x^{4} = x^{6+4}$$. Now, simply add the exponents: $$6+4 = 10$$. Therefore, the simplified expression is: $$x^{10}$$.

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