Use the product rule of exponents to simplify the expression 3*8 and 3*3
To simplify the expression 3*8 using the product rule of exponents, you need to add the exponents since the bases are the same.
Thus, the simplified expression is 3^(1+3) = 3^4 = 81.
To simplify the expression 3*3 using the product rule of exponents, you again add the exponents since the bases are the same.
Thus, the simplified expression is 3^(1+1) = 3^2 = 9.
To simplify the expression 3 * 8 using the product rule of exponents, we can rewrite both numbers as powers of the same base (3).
3 * 8 = 3^1 * 3^3
According to the product rule of exponents, when multiplying two numbers with the same base, we can add their exponents.
So, 3^1 * 3^3 = 3^(1 + 3) = 3^4
Therefore, 3 * 8 simplifies to 3^4.
Now, let's simplify the expression 3 * 3 using the product rule of exponents.
3 * 3 = 3^1 * 3^1
Again, we can apply the product rule of exponents and add the exponents when multiplying two numbers with the same base.
So, 3^1 * 3^1 = 3^(1 + 1) = 3^2
Therefore, 3 * 3 simplifies to 3^2.
To simplify the expression using the product rule of exponents, we need to understand the rule first. The product rule states that for any two numbers with the same base raised to different exponents, we can multiply the base and add the exponents.
Let's use this rule to simplify the expressions:
Expression 3*8:
Here, we have 3 as the base raised to the exponent 8. Since we don't have another expression to combine with, we can consider the exponent of 3 as 1, making it 3^1. Using the product rule, we multiply the base (3) and add the exponents (1+8).
3*8 = 3^(1+8) = 3^9 = 19683
Expression 3*3:
In this expression, we have both 3's as the base, but raised to different exponents, which are both 1. Using the product rule, we multiply the base (3) and add the exponents (1+1).
3*3 = 3^(1+1) = 3^2 = 9
So, using the product rule of exponents, 3*8 simplifies to 19683, and 3*3 simplifies to 9.