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Simplify the following expressions: a) (5pq)2 b) (ab)^x

April 13, 2026Mathematics

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Answers

2 parts

25p^2q^2

a^xb^x

4 steps

Here are the simplifications for the given expressions:

Simplify $(5pq)^2$

Apply the Power of a Product Law, which states that $(xy)^n = x^n y^n$ .
In this case, the bases are 5, $p$ , and $q$ , and the index is 2.
$(5pq)^2 = 5^2 p^2 q^2$
Calculate the value of $5^2$ .
$5^2 = 25$
Substitute the value back into the expression.
$25 p^2 q^2$
The simplified expression is:
$\boxed{25p^2q^2}$

Simplify $(ab)^x$

Apply the Power of a Product Law, which states that $(xy)^n = x^n y^n$ .
In this case, the bases are $a$ and $b$ , and the index is $x$ .
$(ab)^x = a^x b^x$
The simplified expression is:
$\boxed{a^xb^x}$

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