Question

Alabama Connections Academy Exponent Rules Unit Test 7th grade

Answer 1

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:

1. **Product of Powers Rule**: When multiplying two expressions with the same base, you add the exponents.
\[
a^m \times a^n = a^{m+n}
\]

2. **Quotient of Powers Rule**: When dividing two expressions with the same base, you subtract the exponents.
\[
\frac{a^m}{a^n} = a^{m-n}
\]

3. **Power of a Power Rule**: When raising a power to another power, you multiply the exponents.
\[
(a^m)^n = a^{m \times n}
\]

4. **Power of a Product Rule**: When raising a product to a power, you can distribute the exponent to each factor.
\[
(ab)^n = a^n \times b^n
\]

5. **Power of a Quotient Rule**: When raising a quotient to a power, you can distribute the exponent to both the numerator and the denominator.
\[
\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}
\]

6. **Zero Exponent Rule**: Any non-zero base raised to the zero power is equal to one.
\[
a^0 = 1 \quad (a \neq 0)
\]

7. **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

1. Simplify: \(3^2 \times 3^4\)
2. Simplify: \(\frac{2^5}{2^2}\)
3. Simplify: \((5^3)^2\)
4. Simplify: \((xy^2)^3\)
5. Simplify: \(\left(\frac{a^3}{b^2}\right)^2\)
6. Simplify: \(10^0\)
7. Simplify: \(4^{-1}\)

If you need more help, specific examples, or explanations, feel free to ask!