Use the power rule $$ \left(5 p^{7}\right)^{2} $$

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UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ (5*p^7)^2 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(5p^{7}\right)^{2}$$
- step1: Use the properties of exponents:
  $$5^{2}\left(p^{7}\right)^{2}$$
- step2: Evaluate the power:
  $$25p^{14}$$
The power rule states that for any real number $$a$$ and any integers $$m$$ and $$n$$, the following rule holds:

$$
(a^m)^n = a^{m \cdot n}
$$

Using this rule, we can simplify the expression $$(5p^7)^2$$ as follows:

$$
(5p^7)^2 = 5^2 \cdot (p^7)^2 = 25 \cdot p^{7 \cdot 2} = 25p^{14}
$$
$$ (5p^7)^2 = 25p^{14} $$

Use the power rule \[ \left(5 p^{7}\right)^{2} \]

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