Question

when a power is raised to another power in an expression, the exponents are ______.
the rule that states when raising a power to another power, you should multiply the exponents is called the ______ rule.
when encountering an expression such as $(3xy^2)^3$, it is important to apply the power exponent rule to ______ variable within the parentheses.
in $(a^m)^n = a^{m cdot n}$, the base is ______.
a negative exponent means you take the ______ of the base raised to the positive exponent.

Explanation:

For the first statement, according to the power - of - a - power rule in exponents \((a^{m})^{n}=a^{m\times n}\), the exponents are multiplied.
For the second statement, the rule \((a^{m})^{n}=a^{m\times n}\) is known as the power - of - a - power rule.
For the third statement, when applying the power - exponent rule to \((3xy^{2})^{3}\), we need to apply the rule to each factor (the coefficient and each variable) within the parentheses.
For the fourth statement, in the formula \((a^{m})^{n}=a^{m\times n}\), by the definition of the power - of - a - power formula, the base is \(a\).
For the fifth statement, by the definition of negative exponents \(a^{-n}=\frac{1}{a^{n}}\), a negative exponent means you take the reciprocal of the base raised to the positive exponent.

Answer:

1. multiplied
2. power - of - a - power
3. each factor
4. \(a\)
5. reciprocal