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Bot GPT 3.5 1. Simplify the following expression: (4^3)(4^2)
Solution: Using the exponent rule for multiplication, we can add the exponents to simplify the expression. (4^3)(4^2) = 4^(3+2) = 4^5.
2. Simplify the following expression: (2^4)/(2^2)
Solution: Using the exponent rule for division, we can subtract the exponents to simplify the expression. (2^4)/(2^2) = 2^(4-2) = 2^2.
3. Simplify the following expression: (x^2)(x^3)
Solution: Using the exponent rule for multiplication, we can add the exponents to simplify the expression. (x^2)(x^3) = x^(2+3) = x^5.
4. Simplify the following expression: (3^2)^4
Solution: Using the exponent rule for exponentiation, we can multiply the exponents to simplify the expression. (3^2)^4 = 3^(2*4) = 3^8.
5. Simplify the following expression: (a^3)^2
Solution: Using the exponent rule for exponentiation, we can multiply the exponents to simplify the expression. (a^3)^2 = a^(3*2) = a^6.
6. Simplify the following expression: (5^2)(5^3)/(5^4)
Solution: Using the exponent rules for multiplication and division, we can simplify the expression step by step. Firstly, we can add the exponents in the numerator: (5^2)(5^3) = 5^(2+3) = 5^5. Then, we can subtract the exponent in the denominator: 5^5/(5^4) = 5^(5-4) = 5^1 = 5.
7. Simplify the following expression: (b^2)^3(b^4)^2
Solution: Using the exponent rule for exponentiation, we can multiply the exponents in each part of the expression. (b^2)^3(b^4)^2 = b^(2*3) * b^(4*2) = b^6 * b^8 = b^(6+8) = b^14.
8. Simplify the following expression: (2^3 + 2^2)^2
Solution: Using the exponent rule for exponentiation, we can simplify the expression inside the parentheses first. (2^3 + 2^2)^2 = (8 + 4)^2 = 12^2 = 144.
9. Simplify the following expression: (x^3 - x^2)(x^2 + x)
Solution: Using the exponent rule for multiplication, we can use the distributive property to simplify the expression. (x^3 - x^2)(x^2 + x) = x^3*x^2 + x^3*x - x^2*x^2 - x^2*x = x^(3+2) + x^(3+1) - x^(2+2) - x^(2+1) = x^5 + x^4 - x^4 - x^3 = x^5 - x^3.
10. Simplify the following expression: (3^4 - 3^2)/(3^3)
Solution: Using the exponent rules for subtraction and division, we can simplify the expression step by step. Firstly, we can subtract the exponents in the numerator: (3^4 - 3^2) = 3^(4-2) = 3^2. Then, we can divide by the exponent in the denominator: 3^2/(3^3) = 3^(2-3) = 3^(-1) = 1/3.