Exponent rules unit test

Question

Use the product rule of exponents to simplify 5 to the power of 10 and 5 to the power of 5

Answer 1

The product rule of exponents states that when you multiply two exponents with the same base, you can add their exponents. The rule can be expressed as:

\[ a^m \times a^n = a^{m+n} \]

In this case, we have:

\[ 5^{10} \times 5^{5} \]

Using the product rule:

\[ 5^{10} \times 5^{5} = 5^{10 + 5} \]

Now, simplify the exponent:

\[ 5^{10 + 5} = 5^{15} \]

So, \(5^{10} \times 5^{5} = 5^{15}\).