Question

Simplify the expression. Then use a calculator to evaluate the expression. Round the result to the nearest tenth when appropriate. $$ 6.5^{3} \cdot 6.5^{4} $$

Short answer

To simplify and evaluate the expression \(6.5^{3} \cdot 6.5^{4}\), first we add the exponents since the base is the same, which gives us \(6.5^{7}\). Then we use a calculator to find the value of \(6.5^{7}\) and round to the nearest tenth if required.

Step-by-step solution

Identify the base and exponents

The given expression is \(6.5^{3} \cdot 6.5^{4}\). Here, 6.5 is the base and 3 and 4 are the exponents respectively.

Apply the rule of exponents

When multiplying, and your bases are the same, you just add the exponents. According to the rules of exponents, \(a^{m} \cdot a^{n}= a^{m+n}\). So this gives us \(6.5^{3+4} = 6.5^{7}\).

Calculate the value

Let's use a calculator to find the value of \(6.5^{7}\). We keep the result rounded to the nearest tenth if required.