✎ Answers
1. (mn)³
2. (2x⁴b⁵)²
- = (2²)(x⁽⁴⁾⁽²⁾)(b⁽⁵⁾⁽²⁾)
- = 4x⁸b¹⁰
3. (x²)²(3xy²)⁴
- = (x)⁽²⁾⁽²⁾[(3⁴)(x⁴)(y⁽²⁾⁽⁴⁾)]
- = (x⁴)(3⁴)(x⁴)(y⁸)
- = 81(x⁴⁺⁴)(y⁸)
- = 81x⁸y⁸
✎ Explanation:
Let's recall a few rules on exponents.
✍︎ Law #4 of positive integral exponents, also known as the Power of a Product Property.
- It states that if a term is being raised to an exponent, just distribute the exponent to each factor. Thus,
[tex]{\large{\boxed{\tt{(ab)^{n}=a^{n}b^{n}}}}}[/tex]
✍︎ Law #2 of positive integral exponents, also known as the Power of a Power Property.
- It states that if an exponent is being raised to another exponent, just multiply the exponents. Thus,
[tex]{\large{\boxed{\tt{(a^{x})^{n}=a^{xn}}}}}[/tex]
[tex]{\huge{\underline{\sf{Hope\:It\:Helps}}}}[/tex]
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