application of the laws of exponent.
show different ways of simplifying each of the following expression. answer the question that follow.
1. 2^5 * 2^4
2. x^4 * x^7
3. (3^2)^3
4. (m^4)^5
5. (5^3 * 2^2)^2
1. how did you simplify each expression above?
2. what do you think would make it easy to simplify the given expression? why?
1. To simplify each expression, we can apply the laws of exponents:
1. 2^5 * 2^4 = 2^(5+4) = 2^9
2. x^4 * x^7 = x^(4+7) = x^11
3. (3^2)^3 = 3^(2*3) = 3^6
4. (m^4)^5 = m^(4*5) = m^20
5. (5^3 * 2^2)^2 = (5^(3*2) * 2^(2*2))^2 = (5^6 * 2^4)^2
2. It becomes easier to simplify the given expressions when we understand the laws of exponents. In particular, the laws used here are:
- Product rule: a^m * a^n = a^(m+n)
- Power of a power rule: (a^m)^n = a^(m*n)
- Power of a product rule: (a*b)^n = a^n * b^n
By applying these rules, we can combine like terms and simplify the expressions efficiently. With a good understanding of the laws of exponents, simplification becomes systematic and straightforward.
To simplify each of the given expressions, you can apply the laws of exponents. Here are the simplifications for each expression:
1. 2^5 * 2^4:
Using the law of exponents for multiplication, when the bases are the same, you add the exponents. So, 2^5 * 2^4 = 2^(5+4) = 2^9.
2. x^4 * x^7:
Again, using the law of exponents for multiplication, when the bases are the same, you add the exponents. So, x^4 * x^7 = x^(4+7) = x^11.
3. (3^2)^3:
Using the law of exponents for exponentiation, when you raise a power to another exponent, you multiply the exponents. So, (3^2)^3 = 3^(2*3) = 3^6.
4. (m^4)^5:
Similar to the previous expression, when you raise a power to another exponent, you multiply the exponents. So, (m^4)^5 = m^(4*5) = m^20.
5. (5^3 * 2^2)^2:
Using the law of exponents for multiplication inside parentheses, you can raise each term inside the parentheses to the given exponent. So, (5^3 * 2^2)^2 = (5^(3*2)) * (2^(2*2)) = (5^6) * (2^4).
Now, answering your questions:
1. I simplified each expression by applying the laws of exponents. For multiplication, I added the exponents when the bases were the same. For exponentiation, I multiplied the exponents.
2. To make it easier to simplify the given expressions, it is helpful to be familiar with the laws of exponents. Understanding the rules for multiplication and exponentiation can help you quickly determine the simplified form of an expression. Additionally, having a basic knowledge of arithmetic operations, such as addition and multiplication, will enable you to perform the necessary calculations. Regular practice with exponent operations will also improve your speed and accuracy in simplification.
thanks.. :)
simply know and apply the rules of exponents.
e.g.
2. x^4 * x^7 =x^11