Question

Write each expression using a single exponent. Check your answers with a calculator. a. \(5^{3} \cdot 5^{8}\) b. \(9^{2} \cdot 9^{5}\) c. \(7^{4} \cdot 7^{7}\) d. \(7^{5} \cdot 7^{0}\)

Short answer

Question: Simplify the following expressions and check your answer using a calculator: a. \(5^{3} \cdot 5^{8}\) b. \(9^{2} \cdot 9^{5}\) c. \(7^{4} \cdot 7^{7}\) d. \(7^{5} \cdot 7^{0}\) Answer: a. \(5^{11}= 48828125\) b. \(9^{7}= 4782969\) c. \(7^{11}= 1977326743\) d. \(7^{5}= 16807\)

Step-by-step solution

Apply the exponent rule

To solve each expression, we will apply the exponent rule: \(a^{m} \cdot a^{n} = a^{m+n}\). This rule states that when multiplying two exponential expressions with the same base, the exponents can be added. Apply this rule to each expression: a. \(5^{3} \cdot 5^{8}\) b. \(9^{2} \cdot 9^{5}\) c. \(7^{4} \cdot 7^{7}\) d. \(7^{5} \cdot 7^{0}\)

Simplify the expressions

Next, simplify each expression by adding the exponents. a. \(5^{3+8} = 5^{11}\) b. \(9^{2+5} = 9^{7}\) c. \(7^{4+7} = 7^{11}\) d. \(7^{5+0} = 7^{5}\) Now let's check the answers using a calculator.

Check the answers with a calculator

Check each simplified expression: a. \(5^{11} = 48828125\) b. \(9^{7} = 4782969\) c. \(7^{11} = 1977326743\) d. \(7^{5} = 16807\) By following the rule for combining exponents and using a calculator to check the results, we have confirmed that the given expressions have been correctly simplified.