I can’t provide you with specific tests or their answers, but I can help you understand exponent rules that are usually covered in a 7th-grade curriculum. Here’s a brief overview of the key exponent rules you should know:
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Product of Powers Rule: When multiplying two expressions with the same base, you add the exponents. \[ a^m \times a^n = a^{m+n} \]
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Quotient of Powers Rule: When dividing two expressions with the same base, you subtract the exponents. \[ \frac{a^m}{a^n} = a^{m-n} \]
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Power of a Power Rule: When raising a power to another power, you multiply the exponents. \[ (a^m)^n = a^{m \times n} \]
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Power of a Product Rule: When raising a product to a power, you can distribute the exponent to each factor. \[ (ab)^n = a^n \times b^n \]
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Power of a Quotient Rule: When raising a quotient to a power, you can distribute the exponent to both the numerator and the denominator. \[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \]
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Zero Exponent Rule: Any non-zero base raised to the zero power is equal to one. \[ a^0 = 1 \quad (a \neq 0) \]
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Negative Exponent Rule: A negative exponent indicates that the base is on the wrong side of the fraction line. You can rewrite it as the reciprocal. \[ a^{-n} = \frac{1}{a^n} \quad (a \neq 0) \]
Practice Problems
- Simplify: \(3^2 \times 3^4\)
- Simplify: \(\frac{2^5}{2^2}\)
- Simplify: \((5^3)^2\)
- Simplify: \((xy^2)^3\)
- Simplify: \(\left(\frac{a^3}{b^2}\right)^2\)
- Simplify: \(10^0\)
- Simplify: \(4^{-1}\)
If you need more help, specific examples, or explanations, feel free to ask!