Simplify \((ab)^2\).
\((ab)^2\)
\(=(ab)(ab)\)
\(=a\times b\times a\times b\)
\(=a \times a \times b \times b\)
\(=a^{1+1}b^{1+1}\)
\(=a^2b^2 \)
Recall that \(x=x^1\). The exponent of one is implied when one is not shown.
Simplify \((a^6b^9)^3\).
\( (a^6b^9)^3\)
\(=(a^6b^9)(a^6b^9)(a^6b^9)\)
\(=a^{6+6+6}b^{9+9+9}\)
\(=a^{18}b^{27}\)
Alternative Solution
\((a^6b^9)^3\)
\(=(a^6)^3(b^9)^3\)
\(=(a^{(6)(3)})(b^{(9)(3)})\)
Remember to apply the exponent to all powers being multiplied within the brackets.
Simplify \(\left(\dfrac{a}{b}\right)^2\) where \(b\ne0\).
We expand and simplify using the Product Rule.
\(\left(\dfrac{a}{b}\right)^2\)
\(=\left(\dfrac{a}{b}\right) \left(\dfrac{a}{b}\right)\)
\(=\dfrac{a^2}{b^2}\)
We apply the Power of a Power Rule.
\(\begin{align*} &\left(\frac{a}{b}\right)^2 =\frac{a^2}{b^2} \end{align*}\)
Recall
Remember to apply the exponent to all powers being divided within the brackets.
Use the power of a power rule to simplify \((5x^7)^4\).
\( (5x^7)^4\)
\(=(5)^4(x^7)^4\)
\(=5^{(4)}x^{(7)(4)}\)
\(=5^{4}x^{28}\)
\(=625x^{28} \)
Use the power of a power rule to simplify \(\left(\dfrac{a^4}{b^5}\right)^2\).
Distribute the exponent \(2\) to both powers within the brackets.
Use the power of a power rule to simplify \(\left(\dfrac{3^2a^8}{4b^5}\right)^2\).
Note that we can evaluate \(3^4\) as \(81\), and \(4^2\) as \(16\).
Simplify the following expression.
\(((((((exp(r))*(e))*(s))*(s))*(i))*(o))*(n)\)
Enter \(a^b\) as "\(a^{\wedge} b\)" and \(\dfrac{a}{b}\) as "\(a/b\)".
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