Question

rational exponents practice
complete this assessment to review what youve learned. it will not count toward your grade.
rewrite the expression as a product of identical factors to find the product for $100^{\frac{3}{2}}$. submit your answer in simplified form.
(1 point)
\square
check answer remaining attempts : 3

Explanation:

Step1: Recall the exponent rule

The rule for rational exponents is \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\) or can be thought of as taking the \(n\)-th root first and then raising to the \(m\)-th power, or vice versa. For \(100^{\frac{3}{2}}\), we can also rewrite it as a product of identical factors. First, note that \(100 = 10\times10=10^2\), and also, using the property of exponents \(a^{\frac{m}{n}}=(a^{\frac{1}{n}})^m\), so \(100^{\frac{3}{2}}=(100^{\frac{1}{2}})^3\).

Step2: Simplify \(100^{\frac{1}{2}}\)

\(100^{\frac{1}{2}}\) is the square root of 100, and \(\sqrt{100} = 10\) since \(10\times10 = 100\).

Step3: Raise the result to the 3rd power

Now we have \((10)^3\). The product of three 10s: \(10\times10\times10\). Calculating that, \(10\times10 = 100\), and \(100\times10=1000\).

Answer:

\(1000\)