Write 6¹⁰ ÷ 6² as a single power of 6.
Simplify fully 5x³y² * 3x⁴y³
To write 6¹⁰ ÷ 6² as a single power of 6, we need to subtract the exponents.
The given expression can be written as 6^(10-2).
Simplifying, we have 6²⁶.
Therefore, 6¹⁰ ÷ 6² is equal to 6²⁶.
To simplify fully 5x³y² * 3x⁴y³, we need to combine the like terms.
Multiplying the coefficients, we have 5 * 3 = 15.
For the variables, we add the exponents.
For x, we have x³ * x⁴ = x^(3+4) = x⁷.
For y, we have y² * y³ = y^(2+3) = y⁵.
Therefore, 5x³y² * 3x⁴y³ simplifies to 15x⁷y⁵.
To simplify the expression 6¹⁰ ÷ 6² as a single power of 6, we can subtract the exponents.
Since we are dividing two powers with the same base (which is 6), we can subtract the exponents:
6¹⁰ ÷ 6² = 6^(10-2) = 6^8.
Therefore, 6¹⁰ ÷ 6² can be written as a single power of 6, which is 6^8.
Now let's simplify the expression 5x³y² * 3x⁴y³:
To simplify this expression, we can multiply the coefficients (5 * 3 = 15) and combine the variables by adding their exponents.
So, 5x³y² * 3x⁴y³ = 15x^(3+4)y^(2+3).
Simplifying further, we get:
15x^7y^5.
as always, remember that
multiplication adds exponents
division subtracts exponents
6¹⁰ ÷ 6² = 6¹ ÷ 6² = 6^(1-2) = 6^(-1)
But you might have meant
6^10 ÷ 6^2 = 6^(10-2) = 6^8
similarly,
5x³y² * 3x⁴y³ = (5*3) x^(3+4) y^(2+3) = ...