Questions: Question 16 of 25: Step 1 of 1 Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents. (x^2)^5 Correct: 15/25

Solution Steps

To simplify the expression \((x^2)^5\) using the properties of exponents, we can use the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\). Here, \(a = x\), \(m = 2\), and \(n = 5\). Therefore, we multiply the exponents.

• Use the power of a power property to simplify the expression.

To simplify the expression \((x^2)^5\), we use the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\). Here, we have: \[ (x^2)^5 = x^{2 \cdot 5} \]

Now, we calculate the exponent: \[ 2 \cdot 5 = 10 \] Thus, we can rewrite the expression as: \[ (x^2)^5 = x^{10} \]

Final Answer