Question

prealgebra
lesson 34 continued

1. a. $x^{3}$ means _ is a factor _ times.

b. $(x^{3})^{4}$ means _ is a factor _ times. therefore $(x^{3})^{4}=x square$.
c. generalize: $(b^{n})^{m}=b^{square}$.

Explanation:

Step1: Recall exponent meaning

$x^3$ means $x$ is a factor 3 times.

Step2: Analyze $(x^3)^4$

$(x^3)^4$ means $x^3$ is a factor 4 times, and $x^3$ has $x$ as a factor 3 times, so in total $x$ is a factor $3\times4 = 12$ times.

Step3: Generalize

$(b^n)^m$ means $b^n$ is a factor $m$ times, and $b^n$ has $b$ as a factor $n$ times, so $(b^n)^m=b^{n\times m}$.

Answer:

a. $x$, 3
b. $x^3$, 4, 12
c. $n\times m$