Apply All Exponent Rules quiz (Lesson 3.7)
1. Simplify the expression: (2^3)^4.
Solution: To simplify this expression, we can use the exponent rule that states (a^m)^n = a^(m*n). Therefore, (2^3)^4 = 2^(3*4) = 2^12.
2. Simplify the expression: (5^2) * (5^4).
Solution: According to the exponent rule for multiplying exponents with the same base, we can add the exponents. Therefore, (5^2) * (5^4) = 5^(2+4) = 5^6.
3. Simplify the expression: (x^3 * x^5) / x^2.
Solution: By using the exponent rule for dividing exponents with the same base, we subtract the exponents. Hence, (x^3 * x^5) / x^2 = x^(3+5-2) = x^6.
4. Simplify the expression: (3^2)^-2.
Solution: With the exponent rule for negative exponents, we can rewrite this expression as 1 / (3^2)^2. Applying the exponent rule for squaring exponents, we get 1 / 3^(2*2) = 1 / 3^4.
5. Simplify the expression: (a^3)^0.
Solution: According to the exponent rule that any number (except zero) raised to the power of zero is equal to 1, we have (a^3)^0 = 1.
6. Simplify the expression: (4^2)^3 / (4^5)^2.
Solution: By using the exponent rule for dividing exponents with the same base, we subtract the exponents in the numerator and denominator. Thus, (4^2)^3 / (4^5)^2 = 4^(2*3-5*2) = 4^(-4).
7. Simplify the expression: (y^2)^3 * y^4.
Solution: Using the exponent rule for multiplying exponents with the same base, we can add the exponents. Hence, (y^2)^3 * y^4 = y^(2*3+4) = y^10.
8. Simplify the expression: (2^-3) * (2^4).
Solution: Applying the exponent rule for multiplying exponents with the same base, we add the exponents. Therefore, (2^-3) * (2^4) = 2^(-3+4) = 2^1 = 2.
9. Simplify the expression: (x^2)^2 * x^(-4).
Solution: Using the exponent rule for multiplying exponents with the same base, we add the exponents. So, (x^2)^2 * x^(-4) = x^(2*2+(-4)) = x^0 = 1.
10. Simplify the expression: (5^3) / (5^2).
Solution: According to the exponent rule for dividing exponents with the same base, we subtract the exponents. Therefore, (5^3) / (5^2) = 5^(3-2) = 5^1 = 5.