Question

Write your answer as a power or as a product of powers. $$ x \cdot x^{6} $$

Short answer

\(x^7\)

Step-by-step solution

Identify the bases and the exponents

Both the terms have the same base 'x'. The first term 'x' can be written as \(x^1\) (since any number to the power of 1 is the number itself), and the exponent of the second term is 6. So we have \(x^1\) and \(x^6\).

Apply the product rule of exponents

The product rule of exponents states that for any nonzero number 'a' and integers 'm' and 'n', \(a^m \cdot a^n = a^{m+n}\). Using this rule, our equation \(x^1 \cdot x^6\) becomes \(x^{1+6}\).

Simplify the expression

Adding the exponents 1 and 6 gives 7. Therefore, \(x^{1+6}\) becomes \(x^7\).