Simplify $3 a \times a^5$
Answer (2)
We have the expression 3 a × a 5 .
Apply the exponent rule a m × a n = a m + n to combine the terms with a .
Rewrite the expression as 3 × a 1 × a 5 = 3 × a 1 + 5 .
Simplify to get the final answer: 3 a 6 .
Explanation
Understanding the Problem We are asked to simplify the expression 3 a × a 5 . This involves using the properties of exponents to combine the terms with the variable a .
Applying Exponent Rules Recall the property of exponents that states a m × a n = a m + n . In our expression, we have 3 a × a 5 , which can be rewritten as 3 × a 1 × a 5 .
Simplifying the Expression Using the exponent rule, we add the exponents of a : a 1 × a 5 = a 1 + 5 = a 6 . Therefore, the expression becomes 3 a 6 .
Final Answer Thus, the simplified expression is 3 a 6 .
Examples
Understanding how to simplify expressions with exponents is useful in many areas, such as calculating the area or volume of geometric shapes. For example, if you have a cube with side length 2 x , its volume is ( 2 x ) 3 = 8 x 3 . Simplifying expressions helps in determining how quantities change with respect to each other, which is fundamental in physics and engineering.
To simplify 3 a × a 5 , rewrite it as 3 × a 1 × a 5 and apply the exponent rule, resulting in 3 a 6 . The final answer is 3 a 6 .
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