Simplify the following expression. Show your work below
`\left(x^{3}\right)^{5}`
Explain your work
To simplify the expression `\left(x^{3}\right)^{5}`, we need to raise `x^3` to the power of 5.
When we raise a power to another power, we multiply the exponents. Therefore, `x^3` raised to the power of 5 is equal to `x^(3*5)`, which simplifies to `x^15`.
Therefore, the simplified expression is `x^15`.
To simplify the expression `\left(x^{3}\right)^{5}`, we need to apply the power of a power rule. According to this rule, we multiply the exponents when an exponent is raised to another exponent.
In this case, we have a base of x raised to the power of 3, and this whole expression is further raised to the power of 5.
To simplify, we multiply the exponents 3 and 5:
3 * 5 = 15
So, the simplified expression is x^(3*5) = x^15.
Therefore, `\left(x^{3}\right)^{5}` simplifies to x^15.