Question

which expression is equivalent to $5^{-2} \times 5^{5}$?
answer
$\frac{1}{5^{10}}$ $5^{3}$
$\frac{1}{5^{3}}$ $\frac{1}{5^{7}}$

Explanation:

Step1: Recall the exponent rule for multiplication

When multiplying two numbers with the same base, we add the exponents: \(a^m\times a^n = a^{m + n}\). Here, the base \(a = 5\), \(m=-2\), and \(n = 5\).

Step2: Apply the exponent rule

Using the rule \(a^m\times a^n=a^{m + n}\), we substitute the values: \(5^{-2}\times5^{5}=5^{-2 + 5}\).

Step3: Simplify the exponent

Calculate \(-2+5 = 3\). So, \(5^{-2}\times5^{5}=5^{3}\).

Answer:

\(5^3\) (corresponding to the option "5³")